Approximating fixed points of a countable family of strict pseudocontractions in Banach spaces

Abstract

We prove the strong convergence of the modified Mann-type iterative scheme for a countable family of strict pseudocontractions in $q$-uniformly smooth Banach spaces. Our results mainly improve and extend the results announced in [Y. Yao, H. Zhou, Y.-C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J. Appl. Math. Comput. 29 (2009), 383–389].