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COINCIDENCE THEOREMS FOR NONCOMPACT RC-MAPS IN ABSTRACT CONVEX SPACES WITH APPLICATIONS

Nan-Jing Huang|Ming-ge Yang
대한수학회 (The Korean Mathematical Society)|2012.12|대한수학회보 (Bulletin of the KMS)|제49권 제6호|pp. 1147-1161

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참고문헌

키워드

abstract convex spaceminimax inequalitycoincidence theoremalternative theorem$\mathfrak{RC}$-map
주제분류수학

초록

In this paper, a coincidence theorem for a compact RC-map is proved in an abstract convex space. Several more general coincidence theorems for noncompact RC-maps are derived in abstract convex spaces. Some examples are given to illustrate our coincidence theorems. As ap-plications, an alternative theorem concerning the existence of maximal elements, an alternative theorem concerning equilibrium problems and a minimax inequality for three functions are proved in abstract convex spaces.

Abstract

In this paper, a coincidence theorem for a compact RC-map is proved in an abstract convex space. Several more general coincidence theorems for noncompact RC-maps are derived in abstract convex spaces. Some examples are given to illustrate our coincidence theorems. As ap-plications, an alternative theorem concerning the existence of maximal elements, an alternative theorem concerning equilibrium problems and a minimax inequality for three functions are proved in abstract convex spaces.

참고문헌 (26)

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