Strong convergence theorems for a common fixed point of a finite family of Lipschitz hemicontractive-type multivalued mappings

Abstract

Let  $K$ be a non-empty, closed and convex subset of a real Hilbert space $H$. Let $T_i : K \to CB(K), i = 1,2, \ldots, N$, be a finite family of Lipschitz hemicontractive-type mappings with Lipschitz constants $L_i, i=1,2,\ldots, N$, respectively. It is our purpose, in this paper, to introduce  a Halpern type  algorithm which  converges  strongly  to a common fixed point of a finite family of Lipschitz hemicontractive-type  multivalued mappings  under   certain mild conditions. There is no compactness assumption on either the domain set or on the mappings $T_i$ considered.