Strong convergence for a countable family of strict pseudocontractions in q-uniformly smooth Banach spaces

Abstract

We introduce a new iterative algorithm for finding a common fixed point of a countable family of strict pseudocontractions in q-uniformly smooth and uniformly convex Banach spaces. We then prove that the sequence generated by the proposed algorithm converges strongly to a common fixed point of an infinite family of strict pseudocontractions. Our results mainly improve and extend the results announced by Yao et al. [Y. Yao, Y.-C. Liou, G. Marino, Strong convergence of two iterative algorithms for nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl. 2009 (2009) 7 pages. doi:10.1155/2009/279058. Art. ID 279058]. © 2011 Elsevier Ltd. All rights reserved.