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A modified halpern-type iteration algorithm for totally quasi-ϕ-asymptotically nonexpansive mappings with applications
- Source :
-
Applied Mathematics & Computation . Feb2012, Vol. 218 Issue 11, p6489-6497. 9p. - Publication Year :
- 2012
-
Abstract
- 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00963003
- Volume :
- 218
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 70386537
- Full Text :
- https://doi.org/10.1016/j.amc.2011.12.019