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2012 Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces
Juguo Su, Yuchao Tang, Liwei Liu
J. Appl. Math. 2012(SI03): 1-11 (2012). DOI: 10.1155/2012/170540

Abstract

The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

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Juguo Su. Yuchao Tang. Liwei Liu. "Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces." J. Appl. Math. 2012 (SI03) 1 - 11, 2012. https://doi.org/10.1155/2012/170540

Information

Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1251.65085
MathSciNet: MR2948117
Digital Object Identifier: 10.1155/2012/170540

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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