The modified Mann type iterative algorithm for a countable family of totally quasi-φ-asymptotically nonexpansive mappings by the hybrid generalized f-projection method

Abstract

The purpose of this article is to introduce the modified Mann type iterative sequence, using a new technique, by the hybrid generalized f-projection operator for a countable family of totally quasi-φ- asymptotically nonexpansive mappings in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Then we prove that the modified Mann type iterative scheme converges strongly to a common element of the sets of fixed points of the given mappings. Our result extends and improves the results of Li et al. (Comput. Math. Appl. 60:1322-1331, 2010), Takahashi et al. (J. Math. Anal. Appl. 341:276-286, 2008) and many other authors. MSC: 47H05, 47H09, 47H10. © 2013 Saewan et al.; licensee Springer.