Title of article :
Strong convergence theorems for the implicit iteration process for a finite family of hemicontractive mappings in Banach space
Author/Authors :
He، نويسنده , , Huimin and Wang، نويسنده , , Xinshe and Chen، نويسنده , , Rudong and Cakic، نويسنده , , Nenad، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2009
Abstract :
The purpose of this work is to study the following implicit iteration scheme x n = α n x n − 1 + ( 1 − α n ) T n x n , n ≥ 1 , where T n = T n m o d N , 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 } i = 1 N .
Keywords :
Fixed point , Strong convergence , Hemicontractive mappings , Implicit iteration , Banach space
Journal title :
Applied Mathematics Letters
Journal title :
Applied Mathematics Letters