scholarly journals Non-compact random generalized games and random quasi-variational inequalities

1994 ◽  
Vol 7 (4) ◽  
pp. 467-486 ◽  
Author(s):  
Xian-Zhi Yuan
Keyword(s):  
Variational Inequalities ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Countable Number ◽  
Maximal Elements ◽  
Random Fixed Point ◽  
Generalized Game ◽  
Generalized Games ◽  
Person Game

In this paper, existence theorems of random maximal elements, random equilibria for the random one-person game and random generalized game with a countable number of players are given as applications of random fixed point theorems. By employing existence theorems of random generalized games, we deduce the existence of solutions for non-compact random quasi-variational inequalities. These in turn are used to establish several existence theorems of noncompact generalized random quasi-variational inequalities which are either stochastic versions of known deterministic inequalities or refinements of corresponding results known in the literature.

scholarly journals Fixed Points, Maximal Elements and Equilibria of Generalized Games in Abstract Convex Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Yan-Mei Du
Keyword(s):  
Fixed Point ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Recent Literature ◽  
Existence Theorems ◽  
Maximal Elements ◽  
Abstract Convex Space ◽  
Generalized Games ◽  
Set Valued Mappings ◽  
Qualitative Games

We firstly prove some new fixed point theorems for set-valued mappings in noncompact abstract convex space. Next, two existence theorems of maximal elements for class of𝒜C,θmapping and𝒜C,θ-majorized mapping are obtained. As in applications, we establish new equilibria existence theorems for qualitative games and generalized games. Our theorems improve and generalize the most known results in recent literature.

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 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 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 On Maximal Elements with Applications to Abstract Economies, Fixed Point Theory and Eigenvector Problems

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 789
Author(s):  
Liang-Ju Chu ◽  
Wei–Shih Du
Keyword(s):  
Fixed Point ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Abstract Economies ◽  
Coercive Condition ◽  
General Abstract

Two existence theorems of maximal elements in H-spaces are obtained without compactness. More accurately, we deal with the correspondence to be of L -majorized mappings in the setting of noncompact strategy sets but merely requiring a milder coercive condition. As applications, we obtain an equilibrium existence theorem for general abstract economies, a new fixed point theorem, and give a sufficient condition for the existence of solutions of the eigenvector problem (EIVP).

scholarly journals Some Existence Theorems for Nonconvex Variational Inequalities Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Narin Petrot
Keyword(s):  
Variational Inequalities ◽  
Nonsmooth Analysis ◽  
Existence Of Solutions ◽  
Existence Theorems

By using nonsmooth analysis knowledge, we provide the conditions for existence solutions of the variational inequalities problems in nonconvex setting. We also show that the strongly monotonic assumption of the mapping may not need for the existence of solutions. Consequently, the results presented in this paper can be viewed as an improvement and refinement of some known results from the literature.

scholarly journals Fixed Points and Existence Theorems of Maximal Elements with Applications in FC-Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Rong-Hua He
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Maximal Elements ◽  
Minimax Theory ◽  
Coincidence Theorems ◽  
Generalized Equilibrium

We present some fixed point theorems and existence theorems of maximal elements in FC-space from which we derive several coincidence theorems. Applications of these results to generalized equilibrium problems and minimax theory will be given. Our results improve and generalize some recent results.

scholarly journals On measurable multifunctions with stochastic domain

1988 ◽  
Vol 45 (2) ◽  
pp. 204-216 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Hilbert Spaces ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Riesz Representation Theorem ◽  
Random Fixed Point ◽  
Extension Theorems ◽  
Stochastic Version ◽  
Measurable Multifunctions ◽  
Riesz Representation

AbstractIn this paper we prove several random fixed point theorems for multifunctions with a stochastic domain. Then those techniques are used to establish the existence of solutions for random differential inclusions. A useful tool in this process is a stochastic version of the Tietze extension theorems that we prove. Finally we present a stochastic version of the Riesz representation theorem for Hilbert spaces.

scholarly journals Existence theorems for vector variational inequalities

1996 ◽  
Vol 54 (3) ◽  
pp. 473-481 ◽  
Author(s):  
Aris Daniilidis ◽  
Nicolas Hadjisavvas
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Convex Subset ◽  
Variational Inequality Problem ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Multivalued Operator ◽  
Inequality Problem ◽  
Vector Variational Inequality Problem

Given two real Banach spaces X and Y, a closed convex subset K in X, a cone with nonempty interior C in Y and a multivalued operator from K to 2L(x, y), we prove theorems concerning the existence of solutions for the corresponding vector variational inequality problem, that is the existence of some x0 ∈ K such that for every x ∈ K we have A(x − x0) ∉ − int C for some A ∈ Tx0. These results correct previously published ones.

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