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

Title & Authors
COINCIDENCE THEOREMS FOR NONCOMPACT ℜℭ-MAPS IN ABSTRACT CONVEX SPACES WITH APPLICATIONS
Yang, Ming-Ge; Huang, Nan-Jing;

Abstract
In this paper, a coincidence theorem for a compact $\small{{\Re}\mathfrak{C}}$-map is proved in an abstract convex space. Several more general coincidence theorems for noncompact $\small{{\Re}\mathfrak{C}}$-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;$\small{{\Re}\mathfrak{C}}$-map;
Language
English
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