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 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 Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 909-916 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Nonlinear Vector ◽  
Locally Convex

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

scholarly journals Existence of Solutions for Generalized Vector Quasi-Equilibrium Problems by Scalarization Method with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
De-ning Qu ◽  
Cao-zong Cheng
Keyword(s):  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Inclusion Problem ◽  
Quasi Equilibrium ◽  
Nonlinear Scalarization ◽  
Topological Vector Spaces ◽  
Variational Inclusion Problem ◽  
Scalarization Method ◽  
Scalarization Function ◽  
Locally Convex

The aim of this paper is to study generalized vector quasi-equilibrium problems (GVQEPs) by scalarization method in locally convex topological vector spaces. A general nonlinear scalarization function for set-valued mappings is introduced, its main properties are established, and some results on the existence of solutions of the GVQEPs are shown by utilizing the introduced scalarization function. Finally, a vector variational inclusion problem is discussed as an application of the results of GVQEPs.

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.

scholarly journals Maximal elements and equilibria for u-majorised preferences

1994 ◽  
Vol 49 (1) ◽  
pp. 47-54 ◽  
Author(s):  
Kok-Keong Tan ◽  
Xian-Zhi Yuan
Keyword(s):  
Existence Theorem ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
Qualitative Game ◽  
New Type ◽  
General Existence ◽  
Locally Convex

The purpose of this note is to give a general existence theorem for maximal elements for a new type of preference correspondences which are u-majorised. As an application, an existence theorem of equilibria for a qualitative game is obtained in which the preferences are u-majorised with an arbitrary (countable or uncountable) set of players and without compactness assumption on their domains in Hausdorff locally convex topological vector spaces.

scholarly journals Maximal elements and equilibria of generalized games for𝒰-majorized and condensing correspondences

1999 ◽  
Vol 22 (1) ◽  
pp. 179-189 ◽  
Author(s):  
George Xian-Zhi Yuan ◽  
E. Tarafdar
Keyword(s):  
Existence Theorem ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
New Type ◽  
Generalized Games ◽  
Locally Convex ◽  
Qualitative Games

In this paper, we first give an existence theorem of maximal elements for a new type of preference correspondences which are𝒰-majorized. Then some existence theorems for compact (resp., non-compact) qualitative games and generalized games in which the constraint or preference correspondences are𝒰-majorized (resp.,Ψ-condensing) are obtained in locally convex topological vector spaces.

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 Nonlinear Vector Variational Inequality Problems for η-Pseudomonotone Maps

2007 ◽  
Vol 2007 ◽  
pp. 1-6
Author(s):  
A. P. Farajzadeh
Keyword(s):  
Variational Inequality ◽  
Existence Result ◽  
Complementarity Problems ◽  
Vector Variational Inequality ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
New Class ◽  
Pseudomonotone Maps ◽  
Nonlinear Vector

We consider a new class of complementarity problems for η-pseudomonotone maps and obtain an existence result for their solutions in real Hausdorff topological vector spaces. Our results extend the same previous results in this literature.

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