Based on the G-H-KKM selections, some nonempty intersection theorems and their applications to minimax inequalities are presented.

In this paper we consider stochastic equilibrium problems involving parameter of probability measures. Employing the fixed point theorem Knaster, Kuratowski, Mazurkiewicz, and Fan (KKM-Fan), conditions for existence solutions to such are established. We then propose new metric concepts on underlying spaces study some properties corresponding these metrics. Afterwards, sufficient solution mappin...

In this paper, we establish some existence results for strong vector equilibrium problems (for short, SVEP) in topological vector spaces. The solvability of the SVEP is presented using the The second author was in part supported by a grant from IPM (No. 85470015) 220 A.P. Farajzadeh et. al. CUBO 12, 1 (2010) Fan-KKM lemma. These results give a positive answer to an open problem proposed by Chen...

A d-partite hypergraph is called fractionally balanced if there exists a non-negative, not identically zero, function on its edge set that has constant degrees in each vertex side. Using topological version of Hall’s theorem we prove lower bounds the matching number such hypergraphs. These yield rainbow versions KKM for products simplices, which turn are used to obtain some results multiple-cak...

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.