A KKM space is an abstract convex space satisfying the KKM principle. We obtain variants of the KKM principle for KKM spaces related to weakly KKM maps and indicate some applications of them. These results properly generalize the corresponding ones in G-convex spaces and φA-spaces X,D; {φA}A∈〈D〉 . Consequently, results by Balaj 2004, Liu 1991, and Tang et al. 2007 can be properly generalized an...

In set theoretic image recovery, the constraints which do not yield convex sets in the chosen Hilbert solution space cannot be enforced. In some cases, however , such constraints may yield convex sets in other Hilbert spaces. In this paper we introduce a generalized product space formalism, through which constraints that are convex in diierent Hilbert spaces can be combined. A nonconvex problem...

We study fixed point properties for various types of multimaps defined on generalized convex spaces and mutual relations of those properties. We obtain several fixed point theorems for approximable or Kakutani multimaps. Our approach is based on the study of approachable maps initiated mainly by Ben-El-Mechaiekh and other results on generalized convex spaces.

Intersection results for families of H-convex sets in H-spaces are given. These extend known results concerning families of convex sets in topological vector spaces, such as the Berge-Klee intersection theorem and a previous result of the author. MSC 2000. 52A01, 14E20.