The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces

Abstract

In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.  2005 Elsevier Inc. All rights reserved.

The existence of solutions for general variational inequality and applications in FC spaces

“…The existence of solutions and the properties of solutions set for general variational inequality were studied by many authors in linear topologcal spaces (see [1][2][3][4][5][6][7]). These results depend deeply on the linear structure of spaces.…”

Comments on abstract convexity structures on topological spaces

“…In fact, a number of modifications or imitations of the concept have followed; for example, L-spaces [1], spaces having property (H) [2], FC -spaces [3,4], M-spaces and L-spaces in [5,6], and others. It is known that all of such examples belong to the class of φ A -spaces [7,8] and are particular forms of G-convex spaces.…”

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