Coincidence theorems for noncompact $\mathfrak{RC}$-maps in abstract convex spaces with applications
Bull. Korean Math. Soc. 2012 Vol. 49, No. 6, 1147-1161
https://doi.org/10.4134/BKMS.2012.49.6.1147
Published online November 30, 2012
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
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