Best approximation, coincidence and fixed point theorems for set-valued maps in [formula omitted]-trees

Abstract

Suppose X is a closed, convex and geodesically bounded subset of a complete R -tree M , and suppose F : X ⊸ M is an almost lower semicontinuous set-valued map whose values are nonempty closed convex. Suppose also G : X ⊸ X is a continuous, onto quasiconvex set-valued map with compact, convex values. Then there exists x 0 ∈ X such that d ( G ( x 0 ) , F ( x 0 ) ) = inf x ∈ X d ( x , F ( x 0 ) ) . 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.