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...

This paper studies the generalized approximate set-valued equilibrium problems and furnishes some new existence results. The existence results for solutions are derived by using the celebrated KKM theorem and some concepts associated with the semi-continuity of the set-valued mappings such as outer-semicontinuity, inner-semicontinuity, upper-semicontinuity and so forth. The results achieved in ...

This paper concerns equilibrium problems in real metric linear spaces. Considering a modified notion of  upper sign property for bifunctions, we obtain the relationship between the solution sets of the local Minty equilibrium problem and the equilibrium problem, where the technical conditions on $f$ used in the literature are relaxed. The KKM technique is used to generalize and unify some exist...

The present paper is divided into two parts. In the first part, we derive a Fan-KKM type theorem and establish some Fan type geometric properties of convex spaces. By applying our results, we also obtain some coincidence theorems and fixed-point theorems in the setting of convex spaces. The second part deals with the applications of our coincidence theorem to establish some existence results fo...

In this paper, we introduce a class of generalized vector equilibrium problems for set-valued mappings which include a number of vector equilibrium problems, generalized vector variational-like inequality problems and generalized vector variational inequality problems as special cases. By using the KKM-Fan theorem and Nadler’s lemma, we prove the existence of solution to this class of generaliz...