KKM lemmas and minimax inequality theorems in abstract convexity spaces
نویسندگان
چکیده
منابع مشابه
Convexity beyond Vector Spaces, Alternative Theorems and Minimax Equality
The concept of convexlike (concavelike) functions was introduced by Ky Fan (1953), who has proved the rst minimax theorem without linear structure of the underlying spaces. Further extensions or generalizations of this concept have been used later in optimization and decision theory, but the most signiicant applications are in the framework of the game theory, where the strategy spaces are not ...
متن کاملG - H - Kkm Selections with Applications to Minimax Theorems
Based on the G-H-KKM selections, some nonempty intersection theorems and their applications to minimax inequalities are presented.
متن کاملKKM and Ky Fan Theorems in Hyperconvex Metric Spaces
In hyperconvex metric spaces, we introduce Knaster-KuratowskiMazurkiewicz mappings (in short KKM-maps). Then we prove an analogue to Ky Fan fixed point theorem in hyperconvex metric spaces.
متن کاملMinimax Theorems in Probabilistic Metric Spaces
The minimax problem is of fundamental importance in nonlinear analysis and, especially, plays an important role in mathematical economics and game theory. The purpose of this paper is to obtain some minimax theorems for mixed lowerupper semi-continuous functions in probabilistic metric spaces which extend the minimax theorems of von Neumann types [1, 3, 4, 5, 6, 8, 10, 11, 12]. As applications,...
متن کاملFull characterizations of minimax inequality, fixed point theorem, saddle point theorem, and KKM principle in arbitrary topological spaces
This paper provides necessary and sufficient conditions for the existence of solutions for some important problems from optimization and non-linear analysis by replacing two typical conditions—continuity and quasiconcavity with a unique condition, weakening topological vector spaces to arbitrary topological spaces that may be discrete, continuum, non-compact or non-convex. We establish a single...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2013
ISSN: 1687-1812
DOI: 10.1186/1687-1812-2013-209