Positivity (13851292)29(4)
In this paper, we introduce two novel concepts of well-posedness for set optimization problems and present some results in this area. The first main result improves a recent finding in the field without employing the scalarization method. The second one establishes a new form of well-posedness for set optimization problems using a recently introduced scalarization function. To clarify our findings, we also provide corollaries and examples. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.
Fixed Point Theory (15835022)25(1)pp. 163-170
Let C be a nonempty closed bounded (not necessary convex) subset of a Banach space X and let T: C → C be an (α, β)-nonexpansive mapping with α > 0, β > 0 and α + β < 1. In this paper, we show that T has a unique fixed point. Moreover, T is a Picard operator if and only if T is asymptotically regular. © 2024, House of the Book of Science. All rights reserved.
Optimization (10294945)73(5)pp. 1589-1609
In this article, we introduce the notions of l-transfer lower continuous and q-level intersectionally closed for set-valued mappings with respect to the lower set less relation. Then, we obtain some existence results for strict weak l-efficient solutions of such set-valued mappings. Moreover, we prove some existence results for nonconvex set optimization problems via asymptotic analysis tools, in the setting of the Banach spaces equipped with a Hausdorff topology σ coarser than the norm topology. © 2023 Informa UK Limited, trading as Taylor & Francis Group.
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
Journal of Global Optimization (09255001)86(4)pp. 989-1003
In this paper, we extend the definition of the qx-asymptotic functions, for an extended real-valued function defined on the infinite-dimensional topological normed spaces without lower semicontinuity or quasi-convexity condition. As the main result, by using some asymptotic conditions, we obtain sufficient optimality conditions for the existence of solutions to equilibrium problems, under weaker assumptions of continuity and convexity, when the feasible set is an unbounded subset of infinite-dimensional space. Also, as a corollary, we obtain necessary and sufficient optimality conditions for the existence of solutions to equilibrium problems with an unbounded feasible set. Finally, as an application, we establish a result for the existence of solutions to minimization problems. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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.
Bulletin Of The Iranian Mathematical Society (10186301)46(2)pp. 557-571
In this article, we introduce the concepts of multivalued (DL)-type and multivalued α-nonexpansive mappings in the Banach spaces. We show that these two classes of mappings properly contain some important classes of nonlinear mappings. Moreover, we compare the relationship between such classes of mappings and obtain some fixed point results. In addition, we give partial answer to the open question posed by Reich in 1983, about the relationship between fixed point property of multivalued and single-valued nonexpansive mappings. This contribution generalizes and improves some recent results in this context. © 2019, Iranian Mathematical Society.
Journal of Global Optimization (09255001)75(1)pp. 131-141
In this paper, we characterize the nonemptiness of the set of weak minimal elements for a nonempty subset of a linear space. Moreover, we obtain some existence results for a nonconvex set-valued optimization problem under weaker topological conditions. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Taiwanese Journal of Mathematics (10275487)(1)pp. 95-105
We give some new generalized. R-KKM theorems in the nonconvexity setting of topological spaces. As an application we answer a question posed by Isac et al. for the lower and upper bounds equilibrium problem in topological spaces.
