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

Sebsibe Teferi Woldeamanuel, Mengistu Goa Sangago, Habtu Zegeye

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.

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How to Cite this Article:

Sebsibe Teferi Woldeamanuel, Mengistu Goa Sangago, Habtu Zegeye, Strong convergence theorems for a common fixed point of a finite family of Lipschitz hemicontractive-type multivalued mappings, Advances in Fixed Point Theory, Vol 5, No 2 (2015), 228-253

Copyright © 2015 Sebsibe Teferi Woldeamanuel, Mengistu Goa Sangago, Habtu Zegeye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

ISSN: 1927-6303

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