Borel selectors for upper semi-continuous set-valued maps

Inverse Limits of Upper Semi-continuous Set Valued Functions

In this article we define the inverse limit of an inverse sequence (X1, f1), (X2, f2), (X3, f3), . . . where each Xi is a compact Hausdorff space and each fi is an upper semi-continuous function from Xi+1 into 2i . Conditions are given under which the inverse limit is a Hausdorff continuum and examples are given to illustrate the nature of these inverse limits.

Best Proximity Pairs Theorems for Continuous Set-Valued Maps

Structure of the Fixed Point of Condensing Set-Valued Maps

In this paper, we present structure of the fixed point set results for condensing set-valued map. Also, we prove a generalization of the Krasnosel'skii-Perov connectedness principle to the case of condensing set-valued maps.

Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces

This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$

Generalized Convex Set-Valued Maps

The aim of this paper is to show that under a mild semicontinuity assumption (the so-called segmentary epi-closedness), the cone-convex (resp. cone-quasiconvex) set-valued maps can be characterized in terms of weak cone-convexity (resp. weak cone-quasiconvexity), i.e. the notions obtained by replacing in the classical definitions the conditions of type ”for all x, y in the domain and for all t ...