Convergence of the Ishikawa iterate for multi-valued mappings in metric spaces of hyperbolic type

Abstract

Let ($X,d)$ be a metric spaces of hyperbolic type, $C$be a closed and of hyperbolic type subset of $X$ and let $B(C)$ bethe family of all nonempty bounded subsets of $C$. In this papersome results on the convergence of the Ishikawa iteratesassociated with a pair of multi-valued mappings $S,TC\text{toB}(C)$ which satisfy the condition (2.1) below, are obtained.