Strong convergence of a relaxed three-step iterative algorithm for countable families of pseudocontractions

Fixexd point theory and applications

Wei-Qi Deng¹ 

[1] College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, P.R. China

关键词: Lipschitz pseudocontractions;    common fixed points;    countable families of nonlinear operators;    strong convergence;   

DOI  :  10.1186/1687-1812-2013-217

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

An up-to-date method for the approximation of common fixed points of countable families of nonlinear operators is introduced, by which a relaxed three-step iterative algorithm is developed for the class of pseudocontractive mappings, and a strong convergence theorem is established in the framework of Hilbert spaces. Since there is no need to impose uniformity assumption on the involved Lipschitzian and closed mappings, the results improve and extend those announced by Cheng et al. (Fixed Point Theory Appl. 2013:100, 2013) and other authors with the related interest. MSC:47H05, 47H09, 47H10.

【 授权许可】

CC BY