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Strong convergence theorems for the implicit iteration process for a finite family of hemicontractive mappings in Banach space

โœ Scribed by Huimin He; Xinshe Wang; Rudong Chen; Nenad Cakic

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
325 KB
Volume
22
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

The purpose of this work is to study the following implicit iteration scheme

where T n = T nmodN , and to prove several strongly convergent theorems of the iteration for a finite family of hemicontractive mappings in Banach space. Our results extend a recent result of Haiyun Zhou [Haiyun Zhou, Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces, Nonlinear Anal. 68 (2008) 2977-2983] and Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767-773], and we have proved that the sequence {x n } converges strongly to a common fixed point of a finite family of hemicontractive mappings {T i } N i=1 .

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