The Experts below are selected from a list of 18018 Experts worldwide ranked by ideXlab platform
Wen Kaiting - One of the best experts on this subject based on the ideXlab platform.
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Maximal Element theorems for w k majorized mappings in fc spaces and the application to equilibrium of abstract economies
Advances in Mathematics, 2013Co-Authors: Wen KaitingAbstract:In this paper,Maximal Elements theorems for Wk-majorized mappings are established in FC-spaces.As application,existence theorems of equilibrium for qualitative games and abstract economies are obtained in FC-spaces.
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properties of Maximal Element sets for w_f mappings in fc metric spaces and their application to saddle points
Journal of Southwest University, 2013Co-Authors: Wen KaitingAbstract:In this paper,the properties of Maximal Element sets for WF-mappings are studied in noncompact FC-metric spaces.As their application,the properties of Ky Fan sections,solution sets of variational inequalities and saddle point sets are obtained in noncompact FC-metric spaces.
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a Maximal Element theorem in noncompact fc metric spaces with applications to variational inequalities and saddle points
Journal of Bijie University, 2012Co-Authors: Wen KaitingAbstract:In this paper, with the help of the KKM technique, a Maximal Element theorem isestablished in noncompact FC-metric spaces. As applications, a Browder type fixed point theorem, avariational inequality and a saddle point theorem are obtained in noncompact FC-metric spaces. Ourresults unify, improve and generalize some known results in recent reference.
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the Maximal Element theorem in noncompact hyperconvex metric spaces and its application to the minimax question and the saddle point question
Acta Analysis Functionalis Applicata, 2009Co-Authors: Wen KaitingAbstract:An existence theorem for Maximal Elements is established in noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As applications, a Browder-Fan fixed point theorem, a Ky Fan minimax inequality and an existence theorem for saddle points are obtained.
Qamrul Hasan Ansari - One of the best experts on this subject based on the ideXlab platform.
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Preliminaries
Vector Variational Inequalities and Vector Optimization, 2018Co-Authors: Qamrul Hasan Ansari, Elisabeth Köbis, Jen-chih YaoAbstract:This chapter deals with basic definitions from convex analysis and nonlinear analysis, such as convex sets and cones, convex functions and their properties, generalized derivatives, and continuity for set-valued maps. We also gather some known results from fixed point theory for set-valued maps, namely, Nadler’s fixed point theorem, Fan-KKM lemma and its generalizations, Fan section lemma and its generalizations, Browder fixed point theorem and its generalizations, Maximal Element theorems and Kakutani fixed point theorem. A brief introduction of scalar variational inequalities, nonsmooth variational inequalities, generalized variational inequalities and equilibrium problems is given.
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collectively fixed point and Maximal Element theorems in topological semilattice spaces
Applicable Analysis, 2011Co-Authors: Suliman Alhomidan, Qamrul Hasan Ansari, Jen-chih YaoAbstract:In this article, we establish a collectively fixed point theorem and a Maximal Element theorem for a family of multivalued maps in the setting of topological semilattice spaces. As an application of our Maximal Element theorem, we prove the existence of solutions of generalized abstract economies with two constraint correspondences. We consider the system of (vector) quasi-equilibrium problems (in short, (S(V)QEP)) and system of generalized vector quasi-equilibrium problems (in short, (SGVQEP)). We first derive the existence result for a solution of (SQEP) and then by using this result, we prove the existence of a solution of system of a generalized implicit quasi-equilibrium problems. By using existence result for a solution of (SQEP) and weighted sum method, we derive an existence result for solutions of (SVQEP). By using our Maximal Element theorem, we also establish some existence results for the solutions of (SGVQEP). Some applications of our results to constrained Nash equilibrium problem for vector...
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Systems of quasi-variational relations with applications
Nonlinear Analysis: Theory Methods & Applications, 2010Co-Authors: Laijiu Lin, Qamrul Hasan AnsariAbstract:In this paper, we introduce a system of quasi-variational relations (in short, SQVR) and present several examples which show that it is a very general and unified model of several problems. We establish the existence of solutions of SQVP, in general, and several other problems, in particular. As an application of our results, we derive Maximal Element theorems and a collectively fixed point theorem for a family of multivalued maps. As further applications, we study Ky Fan type inequality / inclusion problem for vector valued bifunctions which includes constrained Nash equilibrium problem as a special case. We also present a common fixed point theorem for a family of multivalued maps. The results of this paper improve and generalize several known results on (system of) quasi-equilibrium problems, (system of) quasi-variational inclusions, constrained Nash equilibrium problem, collectively fixed point theorem and KKM type theorems for a family of multivalued maps. Our results also contain several results which appeared in recent literature.
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Fixed point and Maximal Element theorems with applications to abstract economies and minimax inequalities
Journal of Mathematical Analysis and Applications, 2003Co-Authors: Laijiu Lin, Qamrul Hasan Ansari, Li-ping LaiAbstract:In this paper, we establish some fixed point theorems for a family of multivalued maps under mild conditions. By using our fixed point theorems, we derive some Maximal Element theorems for a particular family of multivalued maps, namely the Φ-condensing multivalued maps. As applications of our results, we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences. Further applications of our results are also given to minimax inequalities for a family of functions.
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Generalized vector quasi-equilibrium problems with applications
Journal of Mathematical Analysis and Applications, 2003Co-Authors: Qamrul Hasan Ansari, Fabián Flores-bazánAbstract:In this paper, we consider the generalized vector quasi-equilibrium problem with or without involving Φ-condensing maps and prove the existence of its solution by using known fixed point and Maximal Element theorems. As applications of our results, we derive some existence results for a solution to the vector quasi-optimization problem for nondifferentiable functions and vector quasi-saddle point problem.
Jen-chih Yao - One of the best experts on this subject based on the ideXlab platform.
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Preliminaries
Vector Variational Inequalities and Vector Optimization, 2018Co-Authors: Qamrul Hasan Ansari, Elisabeth Köbis, Jen-chih YaoAbstract:This chapter deals with basic definitions from convex analysis and nonlinear analysis, such as convex sets and cones, convex functions and their properties, generalized derivatives, and continuity for set-valued maps. We also gather some known results from fixed point theory for set-valued maps, namely, Nadler’s fixed point theorem, Fan-KKM lemma and its generalizations, Fan section lemma and its generalizations, Browder fixed point theorem and its generalizations, Maximal Element theorems and Kakutani fixed point theorem. A brief introduction of scalar variational inequalities, nonsmooth variational inequalities, generalized variational inequalities and equilibrium problems is given.
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collectively fixed point and Maximal Element theorems in topological semilattice spaces
Applicable Analysis, 2011Co-Authors: Suliman Alhomidan, Qamrul Hasan Ansari, Jen-chih YaoAbstract:In this article, we establish a collectively fixed point theorem and a Maximal Element theorem for a family of multivalued maps in the setting of topological semilattice spaces. As an application of our Maximal Element theorem, we prove the existence of solutions of generalized abstract economies with two constraint correspondences. We consider the system of (vector) quasi-equilibrium problems (in short, (S(V)QEP)) and system of generalized vector quasi-equilibrium problems (in short, (SGVQEP)). We first derive the existence result for a solution of (SQEP) and then by using this result, we prove the existence of a solution of system of a generalized implicit quasi-equilibrium problems. By using existence result for a solution of (SQEP) and weighted sum method, we derive an existence result for solutions of (SVQEP). By using our Maximal Element theorem, we also establish some existence results for the solutions of (SGVQEP). Some applications of our results to constrained Nash equilibrium problem for vector...
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Maximal Element theorems with applications to generalized games and systems of generalized vector quasi equilibrium problems in g convex spaces
Journal of Optimization Theory and Applications, 2005Co-Authors: X P Ding, Jen-chih YaoAbstract:By applying the Maximal Element theorems on product of G-convex spaces due to the first author, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in G-convex spaces. As applications, some existence theorems of solutions for the system of generalized vector quasiequilibrium problem are established in noncompact product of G-convex spaces. Our results improve and generalize some recent results in the literature to product of G-convex spaces.
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the system of generalized vector equilibrium problems with applications
Journal of Global Optimization, 2002Co-Authors: Qamrul Hasan Ansari, Siegfried Schaible, Jen-chih YaoAbstract:In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a Maximal Element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.
H L Zhang - One of the best experts on this subject based on the ideXlab platform.
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on Maximal Element problem and quasi variational inequality problem in l c metric spaces
Journal of Applied Analysis, 2003Co-Authors: H L ZhangAbstract:In this paper, we give two new Maximal Element theorems in l.c. metric spaces, and as their applications, a new coincidence theo- rem and two new existence theorems of solutions for generalized quasi- variational inequalities are obtained.
Gil Riella - One of the best experts on this subject based on the ideXlab platform.
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Deliberately Stochastic
American Economic Review, 2019Co-Authors: Simone Cerreia-vioglio, David Dillenberger, Pietro Ortoleva, Gil RiellaAbstract:We study stochastic choice as the outcome of deliberate randomization. We derive a general representation of a stochastic choice function where stochasticity allows the agent to achieve from any set the Maximal Element according to her underlying preferences over lotteries. We show that in this model stochasticity in choice captures complementarity between Elements in the set, and thus necessarily implies violations of Regularity/Monotonicity, one of the most common properties of stochastic choice. This feature separates our approach from other models, e.g., Random Utility. (JEL D80, D81)