Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/12358
Title: A modified halpern-type iteration algorithm for totally quasi-φ-asymptotically nonexpansive mappings with applications
Authors: Chang, SS
Lee, HWJ 
Chan, CK 
Zhang, WB
Keywords: Generalized projection
Halpern-type iteration algorithm
Nonexpansive mapping
Quasi-φ- nonexpansive mapping
Quasi-φ-symptotically nonexpansive mapping
Relatively nonexpansive mapping
Total quasi-φ-symptotically nonexpansive mapping
Weak relatively nonexpansive mapping
Issue Date: 2012
Publisher: Elsevier
Source: Applied mathematics and computation, 2012, v. 218, no. 11, p. 6489-6497 How to cite?
Journal: Applied mathematics and computation 
Abstract: The purpose of this article is to modify the Halpern-type iteration algorithm for total quasi-φ-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results of [X.L. Qin, Y.J. Cho, S.M. Kang, H. Y. Zhou, Convergence of a modified Halpern-type iterative algorithm for quasi-φ-nonexpansive mappings, Appl. Math. Lett. 22 (2009) 1051-1055], [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364-2371], [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890-3906], [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and others.
URI: http://hdl.handle.net/10397/12358
ISSN: 0096-3003
EISSN: 1873-5649
DOI: 10.1016/j.amc.2011.12.019
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