Salarian, S.,
Bahlekeh, A.,
Fotouhi, F.S.,
Hamlehdari M.A.,
Salarian S. Publication Date: 2024
Forum Mathematicum (9337741)37pp. 1185-1200
Let (S, n) be a commutative noetherian local ring and let ω ∈ n be non-zerodivisor. This paper is concerned with the two categories of monomorphisms between finitely generated (Gorenstein) projective S-modules, such that their cokernels are annihilated by ω. It is shown that these categories, which will be denoted by Mon(ω, P) and Mon(ω, G), are both Frobenius categories with the same projective objects. It is also proved that the stable category Mon(ω, P) is triangle equivalent to the category of D-branes of type B, DB(ω), which has been introduced by Kontsevich and studied by Orlov. Moreover, it will be observed that the stable categories Mon(ω, P) and Mon(ω, G) are closely related to the singularity category of the factor ring R = S/(ω). Precisely, there is a fully faithful triangle functor from the stable category Mon(ω, G) to Dsg(R), which is dense if and only if R (and so S) are Gorenstein rings. Particularly, it is proved that the density of the restriction of this functor to Mon(ω, P), guarantees the regularity of the ring S. © 2024 Walter de Gruyter GmbH. All rights reserved.
Publication Date: 2012
Topology and its Applications (1668641)159(16)pp. 3453-3460
In this paper, we present some asymptotic stationary point results for topological contraction mappings by relaxing the compactness of the space. Moreover, some classes of topological contractions are characterized. © 2012 Elsevier B.V.
Publication Date: 2005
Journal of Optimization Theory and Applications (223239)126(1)pp. 109-124
In this paper, we apply a new version of the Brézis, Nirenberg, and Stampacchia theorem; we use pseudomonotonicity and some coercivity conditions to establish some existence result for a solution of generalized vector equilibrium problems for multivalued bifunctions. The proper quasiconvexity of multivalued bifunctions is introduced and existence theorems for generalized vector equilibrium problems related to multivalued mappings with the KKM property are obtained. The new results extend and modify various existence theorems for similar problems. © 2005 Springer Science+Business Media, Inc.
Publication Date: 2005
Journal of Optimization Theory and Applications (223239)126(1)pp. 125-136
Existence results for quasimonotone vector equilibrium problems and quasimonotone vector variational inequalities are obtained starting from an existence result for a scalar equilibrium problem involving two quasimonotone bifunctions. These results are established under weaker conditions than in previous works. © 2005 Springer Science+Business Media, Inc.
Publication Date: 2004
Journal of Optimization Theory and Applications (223239)123(2)pp. 349-364
By using quasimonotone and pseudomonotone bifunctions, we derive sufficient conditions which include weak coercivity conditions for existence of equilibrium points. As a consequence, we improve some recent results on the existence of such solutions.
Publication Date: 2003
International Journal of Mathematics and Mathematical Sciences (1611712)2003(51)pp. 3267-3276
We give some new versions of KKM theorem for generalized convex spaces. As an application, we answer a question posed by Isac et al. (1999) for the lower and upper bounds equilibrium problem. © 2003 Hindawi Publishing Corporation. All rights reserved.
Acosta, M.D.,
Fakhar, M.,
Soleimani-mourchehkhorti, M. Publication Date: 2018
Journal of Mathematical Analysis and Applications (0022247X)458(2)pp. 925-936
In this paper, we introduce the notion of the Bishop–Phelps–Bollobás property for numerical radius (BPBp-ν) for a subclass of the space of bounded linear operators. Then, we show that certain subspaces of L(L1(μ)) have the BPBp-ν for every finite measure μ. As a consequence we deduce that the subspaces of finite-rank operators, compact operators and weakly compact operators on L1(μ) have the BPBp-ν. © 2017 Elsevier Inc.
Fakhar, M.,
Mahyarinia m.r., M.R.,
Zafarani j., J. Publication Date: 2018
European Journal of Operational Research (3772217)265(1)pp. 39-48
We introduce a new concept of generalized convexity at a given point for a family of real-valued functions and deduce nonsmooth sufficient optimality conditions for robust (weakly) efficient solutions. In addition, we present a robust duality theory and Mond–Weir type duality for an uncertain multiobjective optimization problem. Furthermore, some nonsmooth saddle-point theorems are obtained under our generalized convexity assumption. Finally we show the viability of our new concept of generalized convexity for robust optimization and portfolio optimization. © 2017 Elsevier B.V.
Publication Date: 2018
Fixed Point Theory (15835022)19(1)pp. 211-218
In this paper the concept of set-valued cyclic Meir–Keeler contraction map is introduced. The existence of best proximity point for such maps on a metric space with the UC property is presented. © 2018, House of the Book of Science. All rights reserved.
Publication Date: 2018
Journal of Nonlinear and Convex Analysis (13454773)19(7)pp. 1189-1198
In this paper, we study the existence of fixed point for asymptotic compact absorbing contraction map and generalized a-set contraction maps. Moreover, we present structure of fixed point set results for this maps. Also, the asymptotic version of the Meir-Keeler, Boyd-Wong, Nadler contractions for the KKM maps on metric space are given. © 2018 Yokohama Publications.
Publication Date: 2018
Nonlinear Studies (13598678)25(3)pp. 689-700
In this paper we show the stability of the Gelfand-Phillips property of order p under tak- ing injective tensor product, compact operators, and Bochner integrable functions. The concept of L-limited sets of order p; is introduced and some characterizations of limited p-convergent operators are given. Also we define the notion of L-limited property of order p and characterize this property in terms of weak compact operators. Furthermore, we give a new dual characterization of the class of weak* p-convergent operators through L-limited sets of order p: Moreover, some characterizations of the Gelfand-Phillips property of order p in terms of limited p-convergent operators are obtained. In addition by applying our results on the limited p-convergent operators, we obtain some characteriza- tions of the Dunford-Pettis* property of order p. © CSP - Cambridge, UK.
Publication Date: 2018
Filomat (3545180)32(6)pp. 2081-2089
In this paper, we study the existence and uniqueness of best proximity points for cyclic Meir– Keeler contraction mappings in metric spaces with the property W-WUC. Also, the existence of best proximity points for set-valued cyclic Meir-Keeler contraction mappings in metric spaces with the property WUC are obtained. © 2018, University of Nis. All rights reserved.
Publication Date: 2017
Bulletin of the Iranian Mathematical Society (10186301)43(1)pp. 131-135
It is well known that every (real or complex) normed linear space L is isometrically embeddable into C(X) for some compact Hausdorff space X. Here X is the closed unit ball of L* (the set of all continuous scalar-valued linear mappings on L) endowed with the weak* topology, which is compact by the Banach-Alaoglu theorem. We prove that the compact Hausdorff space X can indeed be chosen to be the Stone-Čech compactification of L* \ {0}, where L*\ {0} is endowed with the supremum norm topology. © 2017 Iranian Mathematical Society.
Publication Date: 2016
Journal of Nonlinear and Convex Analysis (13454773)17(12)pp. 2483-2500
In this paper, we present a KKM theorem in uniform convex spaces. By using this theorem, several generalized vector quasiequilibrium problems under pseudomonotonicity conditions are studied. Moreover, in the presence of monotonicity, we establish sufficient conditions for well-posedness in new classes of mapping by relaxing some topological requirements. © 2016.
Publication Date: 2016
Journal of Nonlinear and Convex Analysis (13454773)17(3)pp. 569-578
Here, we show that continuous set-valued maps which are generalized set contraction on noncompact topological spaces have a maximal invariant (fixed) set. As an application, we prove the existence and uniqueness of endpoints for topological contraction mappings. Also, we present fractal set results for system of continuous set-valued maps on regular topological spaces. As application of our result, we show how some fixed point theorems can be established from these results. © 2016.
Publication Date: 2015
Journal of Fixed Point Theory and Applications (16617738)17(2)pp. 287-300
On a subset of Banach space which is a locally finite union of closed, convex sets, we extend the Lefschetz fixed point theorem for set-valued mappings. As an application of this result we give a partial answer to Nussbaum’s conjecture for set-valued mappings. © 2014, Springer Basel.
Fakhar, M.,
Khodakhah m.r., M.,
Mazyaki, A.,
Soubeyran a., A.,
Zafarani j., J. Publication Date: 2022
Journal of Global Optimization (9255001)82(1)pp. 161-177
This paper has two aspects. Mathematically, in the context of global optimization, it provides the existence of an optimum of a perturbed optimization problem that generalizes the celebrated Ekeland variational principle and equivalent formulations (Caristi, Takahashi), whenever the perturbations need not satisfy the triangle inequality. Behaviorally, it is a continuation of the recent variational rationality approach of stay (stop) and change (go) human dynamics. It gives sufficient conditions for the existence of traps in a changing environment. In this way it emphasizes even more the striking correspondence between variational analysis in mathematics and variational rationality in psychology and behavioral sciences. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Publication Date: 2021
Optimization Letters (18624472)15(3)pp. 923-931
Different aspects of the KKM Lemma besides its vast applications in nonlinear analysis have been investigated over the years. Some researchers tried to present the KKM results such as generalized L-KKM type theorems in the absence of usual convexity. Here, first we present a counterexample to show that the main results in some generalized KKM type theorems and their consequences are not valid. Afterward, the uniform mapconvex space is introduced and a nonempty intersection result in this space is proved. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Publication Date: 2020
Analysis Mathematica (1333852)46(1)pp. 1-12
In this article we obtain a characterization of the class of p-convergent operators between two Banach spaces in terms of p-(V) subsets of the dual space. Also, for 1 ≤ p < q ≤ ∞, by introducing the concepts of Pelczyński's properties (V)p,q and (V*)p,q, we obtain a condition that ensures that q-convergent operators are p-convergent operators. Some characterizations of the p-Schur property of Banach spaces and their dual spaces are deduced. © 2020, Akadémiai Kiadó, Budapest.
Fakhar, M.,
Mahyarinia m.r., M.R.,
Zafarani j., J. Publication Date: 2019
Optimization (2331934)68(9)pp. 1653-1683
We introduce a new concept of generalized convexity of ‘degree n’ for a multiobjective optimization problem and is compared it to the previous notions of generalized convex functions. Some examples to justify the importance of the term ‘degree n’ are provided. Namely, the conclusions of our results may fail if this term is dropped. By applying our new definition to nonsmooth robust multiobjective optimization problems, we establish the nonsmooth robust optimality conditions and robust duality theory for robust ϵ-quasi-(weakly) efficient solutions. A robust ϵ-Mond-Weir type duality of degree n for an uncertain multi-objective optimization problem under our generalized convexity assumption is presented. Furthermore, we introduce an ϵ-approximate scalar saddle-point and an ϵ-approximate weak vector saddle-point of degree n for the robust multi-objective optimization problem. The relationships between these two concepts with robust ϵ-approximate (KKT) condition and robust ϵ-weakly efficient solutions are also given. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
Publication Date: 2019
Carpathian Journal of Mathematics (15842851)35(3)pp. 407-416
In this article, by using the notions of contingent derivative, contingent epiderivative and generalized contingent epiderivative, we obtain some characterizations of the Lagrange multiplier rule at points which are not necessarily local minima. © 2019, SINUS Association. All rights reserved.
Publication Date: 2019
Journal of Algebra (00218693)540pp. 42-62
We give an explicit description of extended affine root supersystems of type A(l, l) (l not equal 1). (C) 2019 Elsevier Inc. All rights reserved.
Publication Date: 2013
Publications of the Research Institute for Mathematical Sciences (16634926)49(1)pp. 123-153
We offer a presentation for the Weyl group of an affine reflection system R of type A(1) as well as a presentation for the so called hyperbolic Weyl group associated with an affine reflection system of type A(1). Applying these presentations to extended affine Weyl groups, and using a description of the center of the hyperbolic Weyl group, we also give a new finite presentation for an extended affine Weyl group of type A(1). Our presentation for the (hyperbolic) Weyl group of an affine reflection system of type A(1) is the first nontrivial presentation given in this generality, and can be considered as a model for other types.
Publication Date: 2018
Journal of Algebra (00218693)514pp. 25-39
A ring R is called left k-cyclic if every left R-module is a direct sum of indecomposable modules which are homomorphic image of R-R(k). In this paper, we give a characterization of left k-cyclic rings. As a consequence, we give a characterization of left Kothe rings, which is a generalization of Kothe-Cohen-Kaplansky theorem. We also characterize rings which are Morita equivalent to a basic left k-cyclic ring. As a corollary, we show that R is Morita equivalent to a basic left Kothe ring if and only if R is an artinian left multiplicity-free top ring. (C) 2018 Elsevier Inc. All rights reserved.
Publication Date: 2023
Kyoto Journal of Mathematics (21543321)63(1)pp. 1-22
Let (R, m) be a d-dimensional commutative complete Noetherian local ring and A be a Noetherian R-algebra. Motivated by the notion of Cohen-Macaulay Artin algebras of Auslander and Reiten, we say that A is Cohen-Macaulay if there is a finitely generated A-bimodule w that is maximal Cohen-Macaulay over R such that the adjoint pair of functors (w circle times?' -, Hom?' (w, -)) induces quasi-inverse equivalences between the full subcategories of finitely generated A'-modules consisting of modules of finite projective dimension, P degrees degrees(A'), and the modules of finite injective dimension, I degrees degrees(A'), whenever A' = A, Aop. It is proved that such a module w is unique, up to isomorphism, as a A'-module. It is also shown that A is a Cohen-Macaulay algebra if and only if there is a semidualizing A-bimodule w of finite injective dimension and P degrees degrees(A') and I degrees degrees(A') are contained in the Auslander and Bass classes, respectively. We prove that Cohen-Macaulayness behaves well under reduction modulo system of parameters of R. Indeed, it will be observed that if A is a Cohen-Macaulay algebra, then for any system of parameters x = x1, ... , xd of R, the Artin algebra A/xA is Cohen-Macaulay as well. Assume that w is a semidualizing A-bimodule of finite injective dimension that is maximal Cohen-Macaulay as an R-module. It will turn out that A being a Cohen-Macaulay algebra is equivalent to saying that the pair (CM(A'),I degrees degrees(A')) forms a hereditary complete cotorsion theory and the pair (CM(A'op), P degrees degrees(A')) forms a Tor-torsion theory, where CM(A') is the class of all finitely generated A'-modules admitting a right resolution by modules in addw. Finally, it is shown that Cohen-Macaulayness ascends from R to RF and RQ, where F is a finite group and Q is a finite acyclic quiver.
Salarian, S.,
Bahlekeh, A.,
Fotouhi, F.S.,
Nateghi, A.,
Salarian S. Publication Date: 2023
Bulletin Of The Malaysian Mathematical Sciences Society (01266705)46(3)
Let (S, n) be a commutative noetherian local ring and omega is an element of n be non-zerodivisor. This paper deals with the behavior of the category Mon(omega, P) consisting of all monomorphisms between finitely generated projective S-modules with cokernels annihilated by omega. We introduce a homotopy category HMon(omega, P), which is shown to be triangulated. It is proved that this homotopy category embeds into the singularity category of the factor ring R = S/(omega). As an application, not only the existence of almost split sequences ending at indecomposable non-projective objects of Mon(omega, P) is proved, but also the Auslander-Reiten translation, tau Mon(-), is completely recognized. Particularly, it will be observed that any non-projective object of Mon(omega, P) with local endomorphism ring is invariant under the square of the Auslander-Reiten translation.
