Publication Date: 2023
Miskolc Mathematical Notes (17872405)24(3)pp. 1117-1126
In this paper, we obtain a generalization of a fixed point theorem given by Popescu [O. Popescu, Comput. Math. Appl., vol. 62, no. 10, pp. 3912–3919, 2011]. An example is also given to support our main result. © (2023) Miskolc University Press
Publication Date: 2022
Optimization (10294945)71(12)pp. 3695-3708
In this paper, which is deeply inspired from Aussel and Hadjisavvas [On quasimonotone variational inequalities. J Optim Theory Appl. 2004;121:445–450] and Daniilidis and Hadjisavvas [Characterization of nonsmooth semistrictly quasiconvex and strictly quasiconvex functions. J Optim Theory Appl. 1999;102(3):525–536], we study the existence of solutions of the Stampacchia variational inequality for a quasimonotone set-valued vector field on a Hadamard manifold. Moreover, the existence results are obtained under weak assumptions like quasimonotonicity and upper-sign continuity. An application of our results is also given. © 2021 Informa UK Limited, trading as Taylor & Francis Group.
Publication Date: 2021
Journal of Mathematical Analysis and Applications (10960813)502(1)
In this paper, we first obtain a characterization of transfer weakly lower continuous functions. Then, by introducing the class of nearly quasi-closed set-valued mappings, we obtain some characterizations of set-valued mappings whose displacement functions are transfer weakly lower continuous. We also present some fixed point theorems for nearly quasi-closed set-valued mappings which are either nearly almost convex or almost affine. Finally, we construct an almost affine mapping T:[0,1)→R, which is not α-almost convex for any continuous and strictly increasing function α:[0,+∞)→[0,+∞) with α(0)=0. This example gives an affirmative response to the Question 3 of Jachymski (2015) [8]. © 2021 Elsevier Inc.
Publication Date: 2021
Journal of Functional Analysis (10960783)281(10)
The maximal roundness of a metric space is a quantity that arose in the study of embeddings and renormings. In the setting of Banach spaces, it was shown by Enflo that roundness takes on a much simpler form. In this paper we provide simple computations of the roundness of many standard Banach spaces, such as ℓp, the Lebesgue-Bochner spaces ℓp(ℓq) and the Schatten ideals Sp. We also introduce a property that is dual to that of roundness, which we call coroundness, and make explicit the relation of these properties to the geometric concepts of smoothness and convexity of Banach spaces. Building off the work of Enflo, we are then able to provide multiple non-trivial equivalent conditions for a Banach space to possess maximal roundness greater than 1. Using these conditions, we are able to conclude that certain Orlicz spaces possess non-trivial values of roundness and coroundness. Finally, we also use these conditions to provide an explicit example of a 2-dimensional Banach space whose maximal roundness is not equal to that of its dual. © 2021 Elsevier Inc.
Publication Date: 2019
Numerical Functional Analysis and Optimization (15322467)40(5)pp. 603-619
In this article, in the setting of metric spaces we introduce the notions of noncyclic and cyclic Fisher quasi-contraction mappings. We establish the existence of an optimal pair of fixed points for a noncyclic Fisher quasi-contraction mapping and iterative algorithms are furnished to determine such optimal pair of fixed points. For a cyclic Fisher quasi-contraction mapping, we also study the existence of best proximity points. Presented results extend and improve some recent results in the literature. © 2019, © 2019 Taylor & Francis Group, LLC.
Publication Date: 2019
Mediterranean Journal of Mathematics (16605454)16(4)
In this paper, we first introduce a family of geometric constants of a real normed space X and give some results concerning these constants. Then, we give some characterizations of Hilbert spaces and uniformly non-square spaces and obtain sufficient conditions for normal structure related to these constants. © 2019, Springer Nature Switzerland AG.
Publication Date: 2018
Journal of Mathematical Analysis and Applications (10960813)467(2)pp. 1168-1173
In this paper, we define the class of (α,β)-nonexpansive mappings which is properly larger than the class of α-nonexpansive mappings and prove that every (α,β)-nonexpansive mapping T:C→C has an approximate fixed point sequence, where C is a nonempty bounded subset of a Banach space X, α>0 and β≥0. This, in particular, gives an affirmative answer to the open question posed by Ariza-Ruiz and et al. concerning the existence of an approximate fixed point sequence for α-nonexpansive mappings, Ariza-Ruiz et al. (2016) [4]. © 2018 Elsevier Inc.
Publication Date: 2018
Mathematical Inequalities and Applications (13314343)21(1)pp. 287-300
Let (X,) be a real normed space and let θ : (0,∞) → (0,∞) be an increasing function such that t → t/θ(t) is non-decreasing on (0,∞) . For such function, we introduce the notion of θ-angular distance aθ [x,y], where x,y ϵ X \{0}, and showthat X is an inner product space if and only if aθ [x,y] ≤ 2 x-y/θ x+θ y for each x,y ϵ X \{0}. Then, in order to generalize the Dunkl-Williams constant of X [10], we introduce a new geometric constant CF (X) for X wrt F , where F : (0,∞)×(0,∞)→(0,∞) is a given function, and obtain some characterizations of inner product spaces related to the constant CF (X) . Our results generalize and extend various known results in the literature. © ELEMEN , Zagreb.
Publication Date: 2018
Journal of Fixed Point Theory and Applications (16617738)20(1)
Let (X, d) be a metric space, Y be a nonempty subset of X, and let T: Y→ P(X) be a non-self multivalued mapping. In this paper, by a new technique we study the fixed point theory of multivalued mappings under the assumption of the existence of a bounded sequence (xn)n in Y such that Tnxn⊆ Y, for each n∈ N. Our main result generalizes fixed point theorems due to Matkowski (Diss. Math. 127, 1975), Wȩgrzyk (Diss. Math. (Rozprawy Mat.) 201, 1982), Reich and Zaslavski (Fixed Point Theory 8:303–307, 2007), Petruşel et al. (Set-Valued Var. Anal. 23:223–237, 2015) and provides a solution to the problems posed in Petruşel et al. (Set-Valued Var. Anal. 23:223–237, 2015) and Rus and Şerban (Miskolc Math. Notes 17:1021–1031, 2016). © 2018, Springer International Publishing AG, part of Springer Nature.
Publication Date: 2017
Journal of Nonlinear and Convex Analysis (13454773)18(3)pp. 361-368
In this paper, we study P-property and the best proximity point theory. In fact, by using the P-property, we obtain the best proximity counterpart of the many well-known mixed point theorems for multivalued and single valued mappings in the setting of metric spaces and Banach spaces. Presented theorems extend and improve some recent results in the literature. © 2017. Journal of Nonliner and Convex Analysis. All rights reserved.
Publication Date: 2017
Journal of Fixed Point Theory and Applications (16617738)19(4)pp. 2349-2360
In this paper, in the setting of complete metric spaces we establish some fixed point theorems for non-self mappings of contractive type satisfying either the Reich–Zaslavski property or the approximate fixed point property. As applications, we obtain some results in endpoint theory. © 2017, Springer International Publishing.
Publication Date: 2016
SIAM Journal on Optimization (10526234)26(4)pp. 2847-2862
The main goal of this paper is to obtain a generalization of the Weierstrass theorem for transfer weakly lower continuous functions on noncompact topological spaces. To achieve this goal, the notion of a quasi-regular-global-inf (qrgi) function on a topological space is introduced, some equivalent statements are given, and a Weierstrass-Type theorem for such functions is proved. Moreover, the well-posedness of the minimization problem for regular-global-inf (rgi) and qrgi functions is studied. Furthermore, in the setting of reexive Banach spaces the existence of global minimum points of noncoercive qrgi and transfer weakly lower continuous functions are investigated. We also introduce the concept of nearly quasi-convexity of a function, as a generalization of the quasi-convexity notion, and present a result on the minimization problem of these functions. © 2016 Society for Industrial and Applied Mathematics.
Publication Date: 2016
Journal of Fixed Point Theory and Applications (16617738)18(3)pp. 601-607
In this paper, we first show that a Banach space X has weak normal structure if and only if X has the weak fixed point property for nonexpansive mappings with respect to (wrt) orbits. Then, we give a counterexample to show that the Goebel–Karlovitz lemma does not hold for minimal invariant sets of nonexpansive mappings wrt orbits, and we present a modified version of the Goebel–Karlovitz lemma. © 2016, Springer International Publishing.
Publication Date: 2015
Journal of Nonlinear and Convex Analysis (13454773)16(2)pp. 265-271
In this paper, we will introduce first the notions of measure of non-singletonsness (denoted by δ), δ-Cauchy sequence and δ-completeness inthe setting of generalized £-spaces. Main result of the paper is a new endpoint theorem in generalized £-spaces from which we will derive an order-theoretic Cantor theorem in such spaces. Some examples are also given to support our main result. Our results generalize some recent results in the literature. © 2015.
Publication Date: 2015
Communications in Applied Analysis (discontinued) (10832564)19pp. 209-216
In this paper, we present a new and simple approach to coupled fixed point theory of multi-valued maps. By using our method, we first give a very simple proof of the recent coupled fixed point theorems established by Samet and Vetro [B. Samet, C. Vetro, Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Analysis 74(2011), 4260-4268.] Then, we use our technique to present a new tripled fixed point theorem in a general setting. © Dynamic Publishers, Inc.
Publication Date: 2015
Iranian Journal Of Fuzzy Systems (17350654)12(4)pp. 147-153
We consider the concept of fuzzy quasi-contractions initiated by Ćirić in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy H-contractive mappings on M-complete fuzzy metric spaces in the sense of George and Veeramani. The results are illustrated by a representative example. © 2015, University of Sistan and Baluchestan. All rights reserved.
Publication Date: 2014
Fixed Point Theory (15835022)15(1)pp. 87-98
In this paper, by making use of a new class of operators, we establish some existence results of the solution for an extended general variational inequality already considered in the literature. As application, we obtain a new coincidence point theorem in a Hilbert space setting.
Publication Date: 2014
Journal Of Applied Mathematics (16870042)2014
We first introduce a new class of contractive mappings in the setting of metric spaces and then we present certain Greguš type fixed point theorems for such mappings. As an application, we derive certain Greguš type common fixed theorems. Our results extend Greguš fixed point theorem in metric spaces and generalize and unify some related results in the literature. An example is also given to support our main result. © 2014 Marwan A. Kutbi et al.
Publication Date: 2014
Publicationes Mathematicae Debrecen (00333883)85(1-2)pp. 47-58
In this paper we obtain some existence results of solution for general variational inequalities. As applications several coincidence and fixed point results are provided.
Publication Date: 2014
Optimization Letters (18624472)8(2)pp. 581-589
In this paper, we first give an existence and uniqueness common best proximity point theorem for a pair of non-self mappings, one of which weakly dominates the other proximally. Moreover, an algorithm is exhibited to determine such unique common best proximity point. An example is also given to support our main result. Our main result extends and unifies some well-known results in the literature. © 2012 Springer-Verlag Berlin Heidelberg.
Amini harandi, A.,
Amini-harandi a., A.,
Fakhar m., ,
Hajisharifi h.r., ,
Petruşel a., A. Publication Date: 2014
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas (15791505)108(2)pp. 721-732
In this paper, we first introduce a distance space and then give a new fixed point theorem for multi-valued contractions in such spaces. Even in the case of metric spaces, our main theorem unifies and generalizes some recent results in the literature. Some examples are given to show that the fixed point result given here is a genuine generalization. © 2013 Springer-Verlag Italia.
Publication Date: 2014
Miskolc Mathematical Notes (17872405)15(2)pp. 279-285
In this paper, we first introduce the class of generalized nonexpansive mappings in Banach spaces. This class contains both the classes of nonexpansive and α-nonexpansive mappings. In addition, we obtain some fixed point and coincidence point theorems for generalized nonexpansive mappings in uniformly convex Banach spaces. Our results extend some wellknown results in literature. © 2014 Miskolc University Press.
Publication Date: 2014
Fixed Point Theory (15835022)15(2)pp. 351-358
In this paper, we first give a new fixed point theorem for quasi-contraction maps in b-metric spaces which gives a partial answer to a question raised in [S. L. Singh, S. Czerwik, K. Król, A. Singh, Coincidences and fixed points of hybrid contractions, Tamsui Oxf. J. Math. Sci., 24 (2008), 401-416]. Then we derive some fixed point results for contractive type maps. An example is also given to support our main result. Our results extend and improve some fixed point theorems in the literature. © 2014, All Rights reserved.
Publication Date: 2014
Iranian Journal Of Fuzzy Systems (17350654)11(2)pp. 113-120
In this paper, we introduce a new concept of fuzzy generalized contraction and give a fixed point result for such mappings in the setting of fuzzy M-complete metric spaces. We also give an affirmative partial answer to a question posed by Wardowski [D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Set Syst., 222(2013), 108-114]. Some examples are also given to support our main result. © 2014 University of Sistan and Baluchestan. All rights reserved.
Publication Date: 2014
Filomat (03545180)28(6)pp. 1247-1252
Existence theorem for fixed point of mappings satisfying a new generalized contractive condition, involving some well-known contractive conditions of rational type, in ordered metric spaces is proved. Some examples are given which illustrate the value of the obtained results in comparison to some of the existing ones in literature. © 2014, University of Nis. All rights reserved.
Publication Date: 2014
Journal of Nonlinear and Convex Analysis (13454773)15(4)pp. 727-731
In this paper, we first introduce p-quasi-contraction maps in metric spaces for each p ∈ ℕ and then we give a fixed point result for such maps. An example is given to support our result.
Publication Date: 2014
Carpathian Journal of Mathematics (15842851)30(1)pp. 15-16
In this paper, by using a simple technique, we obtain several existence results of the solutions for general variational inequalities of Stampacchia type. We also show, that the existence of a coincidence point of two mappings is equivalent to the existence of the solution of a particular general variational inequality of Stampacchia type. As applications several coincidence and fixed point results are obtained.
Publication Date: 2013
Miskolc Mathematical Notes (17872405)14(1)pp. 11-17
In this paper, we present a fixed point theorem for a new type of contractive mappings. Our main result extends and unifies some well-known results in the literature. © Miskolc University Press.
Publication Date: 2013
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2013
In this paper, we first introduce a cyclic generalized contraction map in metric spaces and give an existence result for a best proximity point of such mappings in the setting of a uniformly convex Banach space. Then we give an existence and uniqueness best proximity point theorem for non-self proximal generalized contractions. Moreover, an algorithm is exhibited to determine such a unique best proximity point. Some examples are also given to support our main results. Our results extend and improve certain recent results in the literature. © 2013 Amini-Harandi et al.; licensee Springer.
Publication Date: 2013
Journal of Global Optimization (09255001)56(4)pp. 1667-1674
In this paper, we introduce a new class of maps, called cyclic strongly quasi-contractions, which contains the cyclic contractions as a subclass. Then we give some convergence and existence results of best proximity point theorems for cyclic strongly quasi-contraction maps. An example is given to support our main results. © 2012 Springer Science+Business Media, LLC.
Publication Date: 2013
Optimization Letters (18624472)7(5)pp. 913-921
In this paper, we give best proximity point theorem for non-self proximal generalized contractions. Moreover, an algorithm is exhibited to determine such an optimal approximate solution designed as a best proximity point. An example is also given to support our main results. © 2012 Springer-Verlag.
Publication Date: 2013
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2013
Certain common fixed point results involving four mappings satisfying generalized contractive conditions on a cone metric type space are obtained. Our results substantially improve and extend a number of known results. An example is given in support of the new results developed here. As an application, we establish the existence of a solution for an implicit integral equation. © 2013 Hussain et al.; licensee Springer.
Publication Date: 2013
Mathematical and Computer Modelling (08957177)57(9-10)pp. 2343-2348
In this paper, we introduce a new, simple and unified approach to coupled and tripled fixed point theory. By using our method, we first give a new coupled fixed point theorem. Then, we use our technique to present a new tripled fixed point result. As an application, we discuss the existence and uniqueness for solution of an initial value problem. Our results extend and improves some recent results in literature. © 2011 Elsevier Ltd.
Publication Date: 2013
Bulletin Of The Iranian Mathematical Society (1017060X)39(1)pp. 165-173
Here, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution. © 2013 Iranian Mathematical Society.
Publication Date: 2013
Rendiconti del Circolo Matematico di Palermo (0009725X)62(3)pp. 367-377
In this paper, we obtain some fixed point theorems for new set-valued contractions in complete metric spaces. Then by using these results and the scalarization method, we present some fixed point theorems for set-valued contractions in complete cone metric spaces without the normality assumption. We also present some examples to support our results. © 2013 Springer-Verlag Italia.
Publication Date: 2013
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2013
In this paper, we first give a new fixed point theorem for generalized Ćirić quasi-contraction maps in generalized metric spaces. Then we derive a common fixed point result for quasi-contractive type maps. Some examples are given to support our results. Our results extend and improve some fixed point and common fixed point theorems in the literature. MSC: 47H10. © 2013 Kiany and Amini-Harandi; licensee Springer.
Amini harandi, A.,
Amini-harandi a., A.,
Fakhar m., ,
Hajisharifi h.r., ,
Hussain, N. Publication Date: 2013
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2013
In this paper, we first introduce two new classes of (ω,δ)- contractions of the first and second kinds and establish some related new fixed point and best proximity point theorems in preordered metric spaces. Our theorems subsume the corresponding recent results of Samet (J. Optim. Theory Appl. (2013), doi:10.1007/s10957-013-0269-9) and extend and generalize many of the well-known results in the literature. An example is also provided to support our main results. ©2013 Amini-Harandi et al.; licensee Springer.
Publication Date: 2012
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2012
In this paper, we prove a coupled fixed point theorem for a multivalued fuzzy contraction mapping in complete Hausdorff fuzzy metric spaces. As an application of the first theorem, a coupled coincidence and coupled common fixed point theorem has been proved for a hybrid pair of multivalued and single-valued mappings. It is worth mentioning that to find coupled coincidence points, we do not employ the condition of continuity of any mapping involved therein. Also, coupled coincidence points are obtained without exploiting any type of commutativity condition. Our results extend, improve, and unify some well-known results in the literature. © 2012 Abbas et al.; licensee Springer.
Publication Date: 2012
Taiwanese Journal of Mathematics (10275487)16(2)pp. 777-785
In this paper, we establish equilibrium version of Ekeland's variational principle without assuming any kind of semicontinuity of the bifunction involved in the formulation of the principle. By using such principle, we derive some existence results for a solution of equilibrium problems with or without compactness assumption on the underlying set. A coercivity condition is introduced to obtain a solution of an equilibrium problem for noncompact case. Our results extend and improve several known results in the literature.
Publication Date: 2012
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2012
In this paper, motivated by the recent work of Wardowski (Fixed Point Theory Appl. 2012:94, 2012), we introduce a new concept of set-valued contraction and prove a fixed point theorem which generalizes some well-known results in the literature. As an application, we derive a new coupled fixed point theorem. Some examples are also given to support our main results. © 2012 Amini-Harandi; licensee Springer.
Publication Date: 2012
Communications in Nonlinear Science and Numerical Simulation (10075704)17(2)pp. 708-712
In this paper, we prove some fixed point theorems for generalized contractions in cone metric spaces. Our theorems extend some results of Suzuki (2008) [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc Amer Math Soc 136(5) (2008), 1861-1869] and Kikkawa and Suzuki (2008) [M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal 69(9) (2008), 2942-2949]. © 2011 Elsevier B.V.
Publication Date: 2012
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2012
By a metric-like space, as a generalization of a partial metric space, we mean a pair (X,σ), where X is a nonempty set and σ : X x X → ℝ satisfies all of the conditions of a metric except that σ (x,x) may be positive for x ∈ X. In this paper, we initiate the fixed point theory in metric-like spaces. As an application, we derive some new fixed point results in partial metric spaces. Our results unify and generalize some well-known results in the literature. © 2012 Amini-Harandi; licensee Springer.
Publication Date: 2011
Nonlinear Analysis, Theory, Methods and Applications (0362546X)74(3)pp. 922-926
In this paper, we first give a best approximation theorem in abstract convex metric spaces. As applications, we then derive some best and coupled best approximations and coupled coincidence point results in normed spaces and hyperconvex metric spaces. © 2010 Elsevier Ltd. All rights reserved.
Publication Date: 2011
Bulletin Of The Iranian Mathematical Society (1017060X)37(4)pp. 229-234
This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets A and B of a Hilbert space H and the set-valued maps F: A → 2 B and G: A 0 → 2 A0, where A 0 = {x ∈ A: {norm of matrix}x - y{norm of matrix} = d(A,B) for some y ∈ B}, best proximity pair theorems provide sufficient conditions that ensure the existence of an x 0 ∈ A such that d(G(x 0), F(x 0)) = d(A,B). © 2011 Iranian Mathematical Society.
Publication Date: 2011
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2011
In this paper, we first present a fixed point theorem for set-valued fuzzy contraction type maps in complete fuzzy metric spaces which extends and improves some well-know results in literature. Then by presenting an endpoint result we initiate endpoint theory for fuzzy contraction maps in fuzzy metric spaces. © 2011 Kiany and Amini-Harandi; licensee Springer.
Publication Date: 2011
Computers and Mathematics with Applications (08981221)61(7)pp. 1891-1897
In this paper, we introduce vector modular spaces and prove the existence of fixed points for generalized quasicontraction maps and discuss their uniqueness in these spaces. Our fixed point theorem, even in the case of modular spaces, extends the main result of Khamsi [M.A. Khamsi, Quasicontraction mappings in modular spaces without Δ2-condition, Fixed Point Theory and Applications 2008, 6 pages, ID 916187]. © 2011 Elsevier Ltd. All rights reserved.
Publication Date: 2011
Applied Mathematics Letters (18735452)24(11)pp. 1791-1794
In this paper, we give a fixed point theorem for set-valued quasi-contraction maps in metric spaces. Our main result improves some well-known results from the literature. © 2011 Elsevier Ltd. All rights reserved.
Publication Date: 2011
Indian Journal of Pure and Applied Mathematics (00195588)42(2)pp. 127-140
In this paper, we introduce and study the generalized implicit vector variational inequality problems with set valued mappings in topological vector spaces. We establish existence theorems for the solution set of these problems be nonempty compact and convex. Our results extend the results by Fang and Huang [ Existence results for generalized implicit vector variational inequalities with multivalued mappings, Indian J. Pure and Appl. Math. 36(2005), 629-640.] © 2011 The Indian National Science Academy.
Publication Date: 2011
Georgian Mathematical Journal (1072947X)18(4)pp. 597-614
Recently, Huang, Li and O'Regan introduced a class of (scalar) generalized f-complementarity problems and three classes of variational inequalities in real Banach spaces for a fixed cone. Our aim is to introduce a vector case of their problems in the real topological vector spaces setting for a moving cone and to generalize their results even in the scalar case. © de Gruyter 2011.
Publication Date: 2010
Nonlinear Analysis, Theory, Methods and Applications (0362546X)72(5)pp. 2238-2242
We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem. © 2009 Elsevier Ltd. All rights reserved.
Publication Date: 2010
Bulletin Of The Iranian Mathematical Society (1017060X)36(1)pp. 69-82
We introduce some new concepts of locally Lipschitz mappings, Clarke subdifferential, approximate convexity and submonotonocity in locally convex spaces. We show that, if f is approximately convex and bounded above, then f is locally Lipschitz. We also prove that a Lipschitz function is approximately convex if and only if its Clarke subdifferential is a submonotone operator. Several properties of approximate convexity are discussed. Our results can be viewed as extensions and refinements of the previously known results from Banach spaces to locally convex spaces. © 2010 Iranian Mathematical Society.
Publication Date: 2010
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2010
The existence of approximate fixed points and approximate endpoints of the multivalued almost I-contractions is established. We also develop quantitative estimates of the sets of approximate fixed points and approximate endpoints for multivalued almost I-contractions. The proved results unify and improve recent results of Amini-Harandi (2010), M. Berinde and V. Berinde (2007), iri (2009), M. Pcurar and R. V. Pcurar (2007) and many others. Copyright © 2010 N. Hussain et al.
Publication Date: 2010
Nonlinear Analysis, Theory, Methods and Applications (0362546X)72(1)pp. 132-134
Suppose (X, d) be a complete metric space, and suppose F : X → C B (X) be a set-valued map satisfies H (F x, F y) ≤ ψ (d (x, y)), for each x, y ∈ X, where ψ : [0, ∞) → [0, ∞) is upper semicontinuous, ψ (t) < t for each t > 0 and satisfies lim inft → ∞ (t - ψ (t)) > 0. Then F has a unique endpoint if and only if F has the approximate endpoint property. © 2009.
Publication Date: 2010
Journal of Optimization Theory and Applications (00223239)146(1)pp. 95-104
This paper deals with some existence theorems for generalized vector variational-like inequalities with set-valued mappings in topological vector spaces. The results presented in this paper generalize and improve some previously known results in the literature. © 2010 Springer Science+Business Media, LLC.
Publication Date: 2010
Nonlinear Analysis, Theory, Methods and Applications (0362546X)72(6)pp. 2891-2895
A new generalized set-valued contraction on topological spaces with respect to a measure of noncompactness is introduced. Two fixed point theorems for the K K M type maps which are either generalized set-contraction or condensing ones are given. Furthermore, applications of these results for existence of coincidence points and maximal elements are deduced. © 2009.
Publication Date: 2010
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2010
We first give some fixed point results for set-valued self-map contractions in complete metric spaces. Then we derive a fixed point theorem for nonself set-valued contractions which are metrically inward. Our results generalize many well-known results in the literature. Copyright © 2010 A. Amini-Harandi and D. O'Regan.
Publication Date: 2010
Computers and Mathematics with Applications (08981221)59(11)pp. 3529-3534
Motivated by the scalarization method in vector optimization theory, we take a new approach to fixed point theory on cone metric spaces. By using our method we prove some fixed point theorems and several common fixed point theorems on cone metric spaces in which the cone need not be normal. Our results improve and generalize many well-known results from the literature. © 2010 Elsevier Ltd. All rights reserved.
Publication Date: 2010
Nonlinear Analysis, Theory, Methods and Applications (0362546X)72(12)pp. 4661-4665
In this paper, we first prove some generalizations of Caristi's fixed point theorem. Then we give some applications to the fixed point theory of weakly contractive set-valued maps and the minimization problem. © 2010 Elsevier Ltd. All rights reserved.
Publication Date: 2009
Nonlinear Analysis, Theory, Methods and Applications (0362546X)70(6)pp. 2453-2456
In this paper, we present a best approximation theorem for set-valued mappings in hyperconvex metric spaces, which generalize the well-known result of Kirk, Sims and Yuan [W.A. Kirk, B. Sims, X.Z. Yuan, The Knaster-Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications, Nonlinear Anal. 39 (2000) 611-627]. © 2008 Elsevier Ltd. All rights reserved.
Publication Date: 2009
Nonlinear Analysis, Theory, Methods and Applications (0362546X)71(11)pp. 5151-5156
Suppose X is a compact admissible subset of a hyperconvex metric spaces M, and suppose F : X {multimap} M is a quasi-lower semicontinuous set-valued map whose values are nonempty admissible. Suppose also G : X {multimap} X is a continuous, onto quasi-convex set-valued map with compact, admissible values. Then there exists an x0 ∈ X such that d (G (x0), F (x0)) = under(inf, x ∈ X) d (x, F (x0)) . As applications, we give some coincidence and fixed point results for weakly inward set-valued maps. Our results, generalize some well-known results in literature. © 2009 Elsevier Ltd. All rights reserved.
Publication Date: 2009
Nonlinear Analysis, Theory, Methods and Applications (0362546X)71(5-6)pp. 1649-1653
Suppose X is a closed, convex and geodesically bounded subset of a complete R-tree M, and suppose F : X {multimap} M is an almost lower semicontinuous set-valued map whose values are nonempty closed convex. Suppose also G : X {multimap} X is a continuous, onto quasiconvex set-valued map with compact, convex values. Then there exists x0 ∈ X such that d (G (x0), F (x0)) = under(inf, x ∈ X) d (x, F (x0)) . As applications, we give some coincidence and fixed point results for weakly inward set-valued maps. Our results generalize some well-known results in literature. © 2009.
Publication Date: 2009
Applied Mathematics Letters (18735452)22(7)pp. 1126-1129
In this work, we consider a generalized nonlinear variational-like inequality problem, in topological vector spaces, and, by using the KKM technique, we prove an existence theorem. Our result extends a theorem of Ahmad and Irfan [R. Ahmad, S.S. Irfan, On the generalized nonlinear variational-like inequality problems, Appl. Math. Lett. 19 (2006) 294-297]. © 2009 Elsevier Ltd. All rights reserved.
Publication Date: 2008
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2008
A best proximity pair for a set-valued map F : A → B with respect to a map g : A → A is defined, and new existence theorems of best proximity pairs for upper semicontinuous set-valued maps with respect to a homeomorphism are proved in hyperconvex metric spaces.
Publication Date: 2008
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2008
A best proximity pair for a set-valued map F : A -○ B with respect to a set-valued map G : A -○ A is defined, and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive retract metric spaces. As an application, we derive a coincidence point theorem. Copyright © 2008 A. Amini-Harandi et al.
Publication Date: 2008
Fixed Point Theory and Algorithms for Sciences and Engineering (16871812)2008
In hyperconvex metric spaces, we first present a coincidence point theorem for condensing set-valued self-maps. Then we consider the best approximation problem and the best proximity problem for set-valued mappings that are condensing. As an application, we derive a coincidence point theorem for nonself-condensing set-valued maps.
Publication Date: 2008
Abstract And Applied Analysis (10853375)2008
We first define upper sign continuity for a set-valued mapping and then we consider two types of generalized vector equilibrium problems in topological vector spaces and provide sufficient conditions under which the solution sets are nonempty and compact. Finally, we give an application of our main results. The paper generalizes and improves results obtained by Fang and Huang in (2005).
Publication Date: 2008
Communications on Applied Nonlinear Analysis (1074133X)15(2)pp. 39-46
In this paper, we first present fixed point theory for continuous condensing set valued nonself maps in hyperconvex metric spaces. Then we establish a fixed point theorem for upper semicontinuous condensing set valued self maps. As an application, we obtain a coincidence point result.
Publication Date: 2008
Journal of Mathematical Analysis and Applications (10960813)344(2)pp. 999-1004
In this paper, generalized vector equilibrium problems are studied and some existence theorems of solutions for these problems in the setting of topological vector spaces are proved. Sufficient conditions for the set of solutions to be compact and convex are given. Our results improve some recent results in this field. © 2008 Elsevier Inc. All rights reserved.
