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.

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 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.

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 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 Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jinlu Li ◽  
Ying Liu ◽  
Hongya Gao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Topological Structure ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Saddle Points ◽  
Order Relation ◽  
Partial Order Relation ◽  
Chain Complete ◽  
Set Valued Mappings

We apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure.

Bound Sets in Partial Orders and the Fixed Point Property

1987 ◽  
Vol 30 (4) ◽  
pp. 421-428 ◽  
Author(s):  
Hartmut Höft
Keyword(s):  
Fixed Point ◽  
Partially Ordered Set ◽  
Fixed Point Theorems ◽  
Ordered Set ◽  
Extension Property ◽  
Fixed Point Property ◽  
Point Property ◽  
Maximal Elements ◽  
Partially Ordered ◽  
Bound Sets

AbstractIn this paper we introduce several properties closely related to the fixed point property of a partially ordered set P: the comparability property, the fixed point property for cones, and the fixed point extension property. We apply these properties to the sets of common bounds of the minimal (maximal) elements of the partially ordered set P in order to derive fixed point theorems for P.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

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