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Wen Kaiting - One of the best experts on this subject based on the ideXlab platform.

Qamrul Hasan Ansari - One of the best experts on this subject based on the ideXlab platform.

  • Preliminaries
    Vector Variational Inequalities and Vector Optimization, 2018
    Co-Authors: Qamrul Hasan Ansari, Elisabeth Köbis, Jen-chih Yao
    Abstract:

    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.

  • collectively fixed point and Maximal Element theorems in topological semilattice spaces
    Applicable Analysis, 2011
    Co-Authors: Suliman Alhomidan, Qamrul Hasan Ansari, Jen-chih Yao
    Abstract:

    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...

  • Systems of quasi-variational relations with applications
    Nonlinear Analysis: Theory Methods & Applications, 2010
    Co-Authors: Laijiu Lin, Qamrul Hasan Ansari
    Abstract:

    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.

  • Fixed point and Maximal Element theorems with applications to abstract economies and minimax inequalities
    Journal of Mathematical Analysis and Applications, 2003
    Co-Authors: Laijiu Lin, Qamrul Hasan Ansari, Li-ping Lai
    Abstract:

    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.

  • Generalized vector quasi-equilibrium problems with applications
    Journal of Mathematical Analysis and Applications, 2003
    Co-Authors: Qamrul Hasan Ansari, Fabián Flores-bazán
    Abstract:

    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.

  • Preliminaries
    Vector Variational Inequalities and Vector Optimization, 2018
    Co-Authors: Qamrul Hasan Ansari, Elisabeth Köbis, Jen-chih Yao
    Abstract:

    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.

  • collectively fixed point and Maximal Element theorems in topological semilattice spaces
    Applicable Analysis, 2011
    Co-Authors: Suliman Alhomidan, Qamrul Hasan Ansari, Jen-chih Yao
    Abstract:

    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...

  • 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, 2005
    Co-Authors: X P Ding, Jen-chih Yao
    Abstract:

    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.

  • the system of generalized vector equilibrium problems with applications
    Journal of Global Optimization, 2002
    Co-Authors: Qamrul Hasan Ansari, Siegfried Schaible, Jen-chih Yao
    Abstract:

    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.

Gil Riella - One of the best experts on this subject based on the ideXlab platform.

  • Deliberately Stochastic
    American Economic Review, 2019
    Co-Authors: Simone Cerreia-vioglio, David Dillenberger, Pietro Ortoleva, Gil Riella
    Abstract:

    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)