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.
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.
Cite this article
S. T. Woldeamanuel, M. G. Sangago, H. Zegeye, Strong convergence theorems for a common fixed point of a finite family of Lipschitz hemicontractive-type multivalued mappings, Adv. Fixed Point Theory 5 (2015), 228–253.
BibTeX
@article{Woldeamanuel2015,
author = {Woldeamanuel, Sebsibe Teferi and Sangago, Mengistu Goa and Zegeye, Habtu},
title = {Strong convergence theorems for a common fixed point of a finite family of Lipschitz hemicontractive-type multivalued mappings},
journal = {Adv. Fixed Point Theory},
volume = {5},
year = {2015},
pages = {228--253},
doi = {}
}