Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2012; 49(6): 1147-1161

Printed November 30, 2012

https://doi.org/10.4134/BKMS.2012.49.6.1147

Copyright © The Korean Mathematical Society.

Coincidence theorems for noncompact $\mathfrak{RC}$-maps in abstract convex spaces with applications

Ming-ge Yang and Nan-jing Huang

Luoyang Normal University, Sichuan University

Abstract

In this paper, a coincidence theorem for a compact $\mathfrak{RC}$-map is proved in an abstract convex space. Several more general coincidence theorems for noncompact $\mathfrak{RC}$-maps are derived in abstract convex spaces. Some examples are given to illustrate our coincidence theorems. As applications, 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.

Keywords: coincidence theorem, alternative theorem, minimax inequality, abstract convex space, $\mathfrak{RC}$-map

MSC numbers: 54H25, 49J53, 49J35