The study of maximal elements, fixed points for -majorized mappings and their applications to minimax and variational inequalities in product topological spaces

1999 ◽  
Vol 37 (7) ◽  
pp. 933-951 ◽  
Author(s):  
Paul Deguire ◽  
Kok Keong Tan ◽  
George Xian-Zhi Yuan
Keyword(s):  
Variational Inequalities ◽  
Fixed Points ◽  
Topological Spaces ◽  
Maximal Elements

scholarly journals Generalized Knaster-Kuratowski-Mazurkiewicz type theorems and applications to minimax inequalities

2017 ◽  
Vol 20 (K2) ◽  
pp. 131-140
Author(s):  
Linh Manh Ha
Keyword(s):  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Applied Mathematics ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Minimax Theorems ◽  
Minimax Inequalities ◽  
Special Cases ◽  
Kkm Mappings ◽  
Definition Of

Knaster-Kuratowski-Mazurkiewicz type theorems play an important role in nonlinear analysis, optimization, and applied mathematics. Since the first well-known result, many international efforts have been made to develop sufficient conditions for the existence of points intersection (and their applications) in increasingly general settings: Gconvex spaces [21, 23], L-convex spaces [12], and FCspaces [8, 9]. Applications of Knaster-Kuratowski-Mazurkiewicz type theorems, especially in existence studies for variational inequalities, equilibrium problems and more general settings have been obtained by many authors, see e.g. recent papers [1, 2, 3, 8, 18, 24, 26] and the references therein. In this paper we propose a definition of generalized KnasterKuratowski-Mazurkiewicz mappings to encompass R-KKM mappings [5], L-KKM mappings [11], T-KKM mappings [18, 19], and many recent existing mappings. Knaster-KuratowskiMazurkiewicz type theorems are established in general topological spaces to generalize known results. As applications, we develop in detail general types of minimax theorems. Our results are shown to improve or include as special cases several recent ones in the literature.

scholarly journals An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 61 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonlinear Transformation ◽  
Generalized Variational Inequalities ◽  
Generalized Variational Inequality ◽  
Suggested Algorithm

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

scholarly journals On D-KKM theorem and its applications

2003 ◽  
Vol 67 (1) ◽  
pp. 67-77 ◽  
Author(s):  
H. K. Pathak ◽  
M. S. Khan
Keyword(s):  
Variational Inequalities ◽  
Existence Results ◽  
Kkm Theorem ◽  
Maximal Elements ◽  
New Class ◽  
Kkm Mappings ◽  
Set Valued Mappings ◽  
Convex Setting

In this paper, we introduce a new class of set-valued mappings in a non-convex setting called D-KKM mappings and prove a general D-KKM theorem. This extends and improves the KKM theorem for several families of set-valued mappings, such as (X, Y), C(X, Y), C (X, Y), C (X, Y) and C (X, Y). In the sequel, we apply our theorem to get some existence results for maximal elements, generalised variational inequalities, and price equilibria.

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