scholarly journals System of Operator Quasi Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Suhel Ahmad Khan
Keyword(s):  
Maximal Element ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Quasi Equilibrium ◽  
Basic Tool ◽  
Maximal Element Theorem ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Element Theorem

We consider a system of operator quasi equilibrium problems and system of generalized quasi operator equilibrium problems in topological vector spaces. Using a maximal element theorem for a family of set-valued mappings as basic tool, we derive some existence theorems for solutions to these problems with and without involving Φ-condensing mappings.

scholarly journals Vector quasi-equilibrium problems

2003 ◽  
Vol 68 (2) ◽  
pp. 295-302 ◽  
Author(s):  
Abdul Khaliq ◽  
Sonam Krishan
Keyword(s):  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Quasi Equilibrium ◽  
Topological Vector Spaces

In this paper we establish existence theorems for vector quasi-equilibrium problems in Hausdorff topological vector spaces both under compactness and noncompactness assumptions.

A New Maximal Theorem in Product GFC-Spaces with Application to Systems of Generalized Mixed Vector Quasiequilibrium Problems

2013 ◽  
Vol 405-408 ◽  
pp. 3151-3154
Author(s):  
Kai Ting Wen
Keyword(s):  
Existence Theorem ◽  
Maximal Element ◽  
Equilibrium Problems ◽  
Quasi Equilibrium ◽  
Quasiequilibrium Problems ◽  
Maximal Element Theorem ◽  
Maximal Theorem ◽  
Vector Quasiequilibrium Problems ◽  
Element Theorem

In this paper, a new maximal element theorem is established in product GFC-spaces. As application, a new existence theorem of solutions for systems of generalized mixed vector quasi-equilibrium problems is obtained.

A minimax inequality with applications to existence of equilibrium points

1993 ◽  
Vol 47 (3) ◽  
pp. 483-503 ◽  
Author(s):  
Kok-Keong Tan ◽  
Zian-Zhi Yuan
Keyword(s):  
Existence Theorems ◽  
Equilibrium Points ◽  
Vector Spaces ◽  
Minimax Inequality ◽  
Approximation Technique ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Topological Vector Spaces ◽  
Person Game ◽  
Element Theorem

A new minimax inequality is first proved. As a consequence, five equivalent fixed point theorems are formulated. Next a theorem concerning the existence of maximal elements for an Lc-majorised correspondence is obtained. By the maximal element theorem, existence theorems of equilibrium points for a non-compact one-person game and for a non-compact qualitative game with Lc-majorised correspondences are given. Using the latter result and employing an “approximation” technique used by Tulcea, we deduce equilibrium existence theorems for a non-compact generalised game with LC correspondences in topological vector spaces and in locally convex topological vector spaces. Our results generalise the corresponding results due to Border, Borglin-Keiding, Chang, Ding-Kim-Tan, Ding-Tan, Shafer-Sonnenschein, Shih-Tan, Toussaint, Tulcea and Yannelis-Prabhakar.

scholarly journals A Maximal Element Theorem inFWC-Spaces and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-18
Author(s):  
Haishu Lu ◽  
Qingwen Hu ◽  
Yulin Miao
Keyword(s):  
Equilibrium Problem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Minimax Problem ◽  
Lower And Upper Bounds ◽  
Weakly Convex ◽  
Maximal Element Theorem ◽  
Variational Relation Problem ◽  
Generalized Equilibrium ◽  
Element Theorem

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem inFWC-spaces. The results represented in this paper unify and extend some known results in the literature.

scholarly journals The Hierarchical Minimax Inequalities for Set-Valued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yen-Cherng Lin ◽  
Chin-Tzong Pang
Keyword(s):  
Equilibrium Problems ◽  
Vector Spaces ◽  
Minimax Inequalities ◽  
Topological Vector Spaces ◽  
Set Valued Mappings

We study the minimax inequalities for set-valued mappings with hierarchical process and propose two versions of minimax inequalities in topological vector spaces settings. As applications, we discuss the existent results of solutions for set equilibrium problems. Some examples are given to illustrate the established results.

scholarly journals Existence of solutions for a system of quasi-variational relation problems and some applications

2015 ◽  
Vol 31 (1) ◽  
pp. 135-142
Author(s):  
ZHE YANG ◽  
Keyword(s):  
Nash Equilibrium ◽  
Maximal Element ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Quasi Equilibrium ◽  
Variational Inclusions ◽  
New Class

In this paper, we study the existence of solutions for a new class of systems of quasi-variational relation problems on different domains. As applications, we obtain existence theorems of solutions for systems of quasi-variational inclusions, systems of quasi-equilibrium problems, systems of generalized maximal element problems, systems of generalized KKM problems and systems of generalized quasi-Nash equilibrium problems on different domains. The results of this paper improve and generalize several known results on variational relation problems.

scholarly journals Existence of solutions for a new version of generalized operator equilibrium problems

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4701-4710
Author(s):  
Ardeshir Karamian ◽  
Rahmatollah Lashkaripour
Keyword(s):  
Existence Theorem ◽  
Maximal Element ◽  
Existence Result ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Nonlinear Scalarization ◽  
Topological Vector Spaces ◽  
Generalized Operator ◽  
Ky Fan

In this paper, a system of generalized operator equilibrium problems(for short, SGOEP) in the setting of topological vector spaces is introduced. Applying some properties of the nonlinear scalarization mapping and the maximal element lemma an existence theorem for SGOEP is proved. Moreover, using Ky Fan?s lemma an existence result for the generalized operator equilibrium problem(for short, GOEP) is established. The results of the paper can be viewed as a generalization and improvement of the corresponding results given in [1,2,5,8].

scholarly journals Equilibrium points of random generalized games

1998 ◽  
Vol 21 (4) ◽  
pp. 791-800 ◽  
Author(s):  
E. Tarafdar ◽  
Xian-Zhi Yuan
Keyword(s):  
Existence Theorem ◽  
Existence Theorems ◽  
Equilibrium Points ◽  
Lower Semicontinuous ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Topological Vector Spaces ◽  
Generalized Games ◽  
Random Games

In this paper, the concepts of random maximal elements, random equilibria and random generalized games are described. Secondly by measurable selection theorem, some existence theorems of random maximal elements forLc-majorized correspondences are obtained. Then we prove existence theorems of random equilibria for non-compact one-person random games. Finally, a random equilibrium existence theorem for non-compact random generalized games (resp., random abstract economics) in topological vector spaces and a random equilibrium existence theorem of non-compact random games in locally convex topological vector spaces in which the constraint mappings are lower semicontinuous with countable number of players (resp., agents) are given. Our results are stochastic versions of corresponding results in the recent literatures.

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