Collectively fixed point and maximal element theorems in topological semilattice spaces

2011 ◽  
Vol 90 (6) ◽  
pp. 865-888 ◽  
Author(s):  
S. Al-Homidan ◽  
Q.H. Ansari ◽  
J.-C. Yao
Keyword(s):  
Fixed Point ◽  
Maximal Element ◽  
Topological Semilattice ◽  
Collectively Fixed Point

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.

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 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].

An RS-KKM Theorem in FC-Metric Spaces with the Application to Fixed Points

2013 ◽  
Vol 838-841 ◽  
pp. 2215-2218
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Maximal Element ◽  
Metric Spaces ◽  
Recent Literature ◽  
Kkm Theorem ◽  
Kkm Mappings ◽  
Section Theorem ◽  
Element Theorem ◽  
Ky Fan

In this paper, RS-KKM mappings are introduced and an RS-KKM theorem is established in noncompact complete FC-metric spaces. As applications, a Ky Fan section theorem, a maximal element theorem and a Fan-Browder type fixed point theorem are obtained in noncompact complete FC-metric spaces. These results unify, improve and generalize some known results in recent literature.

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