On Equilibrium for Abstract Economies in GFC-Spaces

2014 ◽  
Vol 587-589 ◽  
pp. 2279-2284
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Kkm Mapping ◽  
Equilibrium Existence ◽  
Abstract Economies ◽  
Element Theorem ◽  
Qualitative Games

In this paper, the GFC-KKM mapping is introduced and GFC-KKM theorems are established in GFC-spaces. As applications, a fixed point theorem and maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, equilibrium existence theorems for qualitative games and abstract economies are yielded in GFC-spaces.

A fuzzy fixed-point theorem and its applications to maximal elements and Nash equilibria in noncompact CAT(0) spaces

2022 ◽  
pp. 1-18
Author(s):  
Haishu Lu ◽  
Rong Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Equilibrium Points ◽  
Maximal Elements ◽  
Nash Equilibrium Points ◽  
Fuzzy Fixed Point ◽  
Qualitative Games

In this paper, based on the KKM method, we prove a new fuzzy fixed-point theorem in noncompact CAT(0) spaces. As applications of this fixed-point theorem, we obtain some existence theorems of fuzzy maximal element points. Finally, we utilize these fuzzy maximal element theorems to establish some new existence theorems of Nash equilibrium points for generalized fuzzy noncooperative games and fuzzy noncooperative qualitative games in noncompact CAT(0) spaces. The results obtained in this paper generalize and extend many known results in the existing literature.

scholarly journals A Collectively Fixed Point Theorem in Abstract Convex Spaces and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Haishu Lu ◽  
Qingwen Hu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Theorems ◽  
Abstract Economies ◽  
Collectively Fixed Point ◽  
Convex Spaces

The main purpose of this paper is to establish a new collectively fixed point theorem in noncompact abstract convex spaces. As applications of this theorem, we obtain some new existence theorems of equilibria for generalized abstract economies in noncompact abstract convex spaces.

scholarly journals A selection theorem and its applications

1992 ◽  
Vol 46 (2) ◽  
pp. 205-212 ◽  
Author(s):  
Xie Ping Ding ◽  
Won Kyu Kim ◽  
Kok-Keong Tan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Product Space ◽  
Existence Theorems ◽  
Intersection Theorem ◽  
Selection Theorem ◽  
Equilibrium Existence ◽  
Abstract Economy

In this paper, we first prove an improved version of the selection theorem of Yannelis-Prabhakar and next prove a fixed point theorem in a non-compact product space. As applications, an intersection theorem and two equilibrium existence theorems for a non-compact abstract economy are given.

scholarly journals Approximate fixed points on almost convex sets

2004 ◽  
Vol 35 (3) ◽  
pp. 255-260
Author(s):  
J. E. C. Lope ◽  
R. M. Rey ◽  
M. Roque ◽  
P. W. Sy
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Maximal Element ◽  
Convex Sets ◽  
Maximal Element Theorem ◽  
Approximate Fixed Point ◽  
Almost Convex ◽  
Element Theorem

In this paper, we deduce a maximal element theorem on multimaps and an approximate fixed point theorem on almost convex sets. This generalizes the well-known Himmelberg fixed point theorem and also unifies recent results of Park and Tan [14] %cite{tan2} and Sy and Park [16].

The Equilibrium Existence for Constrained Multiobjective Games in GFC-Spaces

2014 ◽  
Vol 1065-1069 ◽  
pp. 3450-3454
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Existence Theorems ◽  
Equilibrium Existence ◽  
Quasiequilibrium Problems ◽  
In Virtue Of

In this paper, in virtue of a Browder type fixed point theorem in GFC-spaces, equilibrium existence theorems for general quasiequilibrium problems and quasiequilibrium problems are obtained. As application, an existence theorem of weighted Nash-equilibriums for constrained multiobjective games is yielded in GFC-spaces.

scholarly journals New Generalized Ekeland’s Variational Principle, Critical Point Theorems and Common Fuzzy Fixed Point Theorems Induced by Lin-Du’s Abstract Maximal Element Principle

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 11
Author(s):  
Junjian Zhao ◽  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Critical Point ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle ◽  
Fuzzy Fixed Point ◽  
Element Theorem

In this paper, by applying the abstract maximal element principle of Lin and Du, we present some new existence theorems related with critical point theorem, maximal element theorem, generalized Ekeland’s variational principle and common (fuzzy) fixed point theorem for essential distances.

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).

The Equilibrium Existence Theorem for Systems of General Quasiequilibrium Problems in GFC-Spaces

2014 ◽  
Vol 556-562 ◽  
pp. 4128-4132
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Existence Theorem ◽  
Maximal Element ◽  
Kkm Mapping ◽  
Kkm Theorem ◽  
Equilibrium Existence ◽  
Quasiequilibrium Problems ◽  
Maximal Element Theorem ◽  
Matching Theorem ◽  
Element Theorem

In this paper, the GFC-KKM mapping is introduced and a GFC-KKM theorem is established in GFC-spaces. As applications, a matching theorem and a maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, an equilibrium existence theorem for systems of general quasiequilibrium problems is yielded in GFC-spaces.

scholarly journals New Results and Generalizations for Approximate Fixed Point Property and Their Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Shih Du ◽  
Farshid Khojasteh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Fixed Point Property ◽  
Point Property ◽  
Approximate Fixed Point ◽  
Nadler’S Fixed Point Theorem ◽  
Approximate Fixed Point Property

We first introduce the concept of manageable functions and then prove some new existence theorems related to approximate fixed point property for manageable functions andα-admissible multivalued maps. As applications of our results, some new fixed point theorems which generalize and improve Du's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and Nadler's fixed point theorem and some well-known results in the literature are given.

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