© Hindawi Publishing Corp. NONEMPTY INTERSECTION THEOREMS MINIMAX THEOREMS WITH APPLICATIONS IN GENERALIZED INTERVAL SPACES

Abstract. We establish some new topological types of nonempty intersection theorems in more general topological spaces without linear structure. As applications, we utilize results to study the minimax problems, coincidence problems, and economy equilibrium problems in generalized interval spaces and some new results are obtained. 2000 Mathematics Subject Classification. 49K35, 54D20, 54D05, 54H25. 1. Introduction and preliminaries. Recently, some versions of Fan’s KKM theorem and Fan’s minimax theorem in topological spaces without linear structure have been considered by Cheng and Lin [2], Lin et al. [10, 11], and Tian [14]. The purpose of this paper is first to introduce and establish a class of more general topological space-generalized interval space, which has no linear structure and contains H-space, inter