Best approximation, coincidence and fixed point theorems for set-valued maps in RR-trees

Suppose XX is a closed, convex and geodesically bounded subset of a complete RR-tree MM, and suppose F:X⊸MF:X⊸M is an almost lower semicontinuous set-valued map whose values are nonempty closed convex. Suppose also G:X⊸XG:X⊸X is a continuous, onto quasiconvex set-valued map with compact, convex values. Then there exists x0∈Xx0∈X such that d(G(x0),F(x0))=infx∈Xd(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.