Best approximation, coincidence and fixed point theorems for quasi-lower semicontinuous set-valued maps in hyperconvex metric spaces

Abstract

Suppose X is a compact admissible subset of a hyperconvex metric spaces M, and suppose F : X {multimap} M is a quasi-lower semicontinuous set-valued map whose values are nonempty admissible. Suppose also G : X {multimap} X is a continuous, onto quasi-convex set-valued map with compact, admissible values. Then there exists an x0 ∈ X such that d (G (x0), F (x0)) = under(inf, x ∈ X) d (x, F (x0)) . As applications, we give some coincidence and fixed point results for weakly inward set-valued maps. Our results, generalize some well-known results in literature. © 2009 Elsevier Ltd. All rights reserved.