Opuscula Math. 34, no. 1 (2014), 67-79
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].
Keywords: common fixed points, convergence theorem, modified Mann iteration, strict pseudocontractions, \(q\)-uniformly smooth Banach spaces.
Mathematics Subject Classification: 47H09, 47H10.