A modified Halpern-type iteration algorithm for quasi-ϕ -asymptotically nonexpansive mappings and applications

The purpose of this article is to modify the Halpern-type iteration algorithm for 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 resul...

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Vydáno v:Mathematica Slovaca Ročník 64; číslo 1; s. 175 - 186
Hlavní autoři: Tang, Yong Kun, Chang, Shih-sen, Wang, Lin, Zhao, Y. H., Chan, Chi Kin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Heidelberg Versita 01.02.2014
Témata:
Algebra
generalized projection
Mathematics
Mathematics and Statistics
Primary 47J05, 47H09, 49J25
quasi-ϕ-nonexpansive mapping
quasi-ϕ-symptotically nonexpansive mapping
relatively nonexpansive mapping
weak relatively nonexpansive mapping
weak relatively nonexpansive mapping
nonexpansive mapping
quasi
symptotically nonexpansive mapping
relatively nonexpansive mapping
Primary 47J05, 47H09, 49J25
generalized projection
ISSN:0139-9918, 1337-2211, 1337-2211
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Popis
Shrnutí:The purpose of this article is to modify the Halpern-type iteration algorithm for 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 Qin et al. [ Convergence of a modified Halpern-type iterative algorithm for quasi-ϕ-nonexpansive mappings , Appl. Math. Lett. 22 (2009), 1051–1055], Wang et al. [ 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], Su et al. [ Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications , Nonlinear Anal. 73 (2010), 3890–3906], Nartinez-Yanes et al}. [ Strong convergence of the CQ method for fixed point iteration processes , Nonlinear Anal. 64 (2006), 2400–2411], and others.
ISSN:0139-9918
1337-2211
1337-2211
DOI:10.2478/s12175-013-0194-2