On the approximation problem of fixed points for asymptotically nonexpansive mappings
type: Item
instance of: scholarly article
title: On the approximation problem of fixed points for asymptotically nonexpansive mappings
zbMATH Open document ID: 1034.47039
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2001-01-01T00:00:00Z
review text: This article deals with the Ishikawa and Mann approximations with errors \[ x_{n+1}= (1-\alpha_n-\gamma_n) x_n+\alpha_nT^ny_n +\gamma_nw_n,\quad y_n=(1-\beta_n-\delta_n)x_n+ \beta_nT^nx_n+ \delta_n z_n, \tag{1} \] \[ x_{n+1}= (1-\alpha_n -\gamma_n)x_n+ \alpha_n T^nx_n+ \gamma_n w_n,\tag{2} \] for asymptotically nonexpansive mappings \(T\) in a real uniformly convex Banach space \(E\). The author formulates sufficient conditions on \(\alpha_n,\beta_n, \gamma_n, \delta_n\) and Lipschitzian constants \(k_n\) of \(T^n\) for the convergence of approximations (1) and (2) and states that the corresponding theorems improve and generalize results by K. Goebel and W. A. Kirk, B. E. Rhoades, J. Schu and correct results by Z. Y. Huang.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1785895
zbMATH Keywords: Ishikawa and Mann approximations with errors
zbMATH Keywords: nonexpansive mappings
zbMATH Keywords: uniformly convex Banach space
zbMATH Keywords: convergence
author: Shihsen Chang
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1785895