Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Hor...

We extend the concept of relaxed α-monotonicity to mixed relaxed α-β-monotonicity. The concept of mixed relaxed α-β-monotonicity is more general than many existing concepts of monotonicities. Finally, we apply this concept and well known KKM-theory to obtain the solution of generalized equilibrium problem.

It is known (see [5, 6]) that when K is a closed convex cone, problems NCP( f ,K) and VI( f ,K) are equivalent. To study the existence of solutions of the NCP( f ,K) and VI( f ,K) problems, many authors have used the techniques of KKM mappings, and the Fan-KKM theorem from fixed point theory (see [1, 5, 6, 7, 8, 9, 10]). In case B is a Hilbert space, Isac and other authors have used the notion ...

We give some new versions of KKM theorem for generalized convex spaces. As an application, we answer a question posed by Isac et al. (1999) for the lower and upper bounds equilibrium problem.

In this paper, we establish two matching theorems involving three maps. As applications, KKM type theorems, intersections theorems, analytic alternatives and minimax inequalities are obtained. AMS subject classifications: 54H25, 54C60

This paper is devoted to the existence of solutions for generalized variational like inequalities with fuzzy mappings in topological vector spaces by using a particular form of the generalized KKM-Theorem.

The concept of generalized KKM maps was initiated by Kassay-Kolumbán in 1990 and Chang-Zhang 1991. Recently, Balaj his colleagues extended w.r.t. a multimap to weak applied them various problems the theory. However, their results are mainly concerned within realm topological vector spaces. Our aim this article is extend some abstract convex Some related facts also discussed.