An iterative approximation of fixed points of strictly pseudocontractive mappings in Banach spaces

Abstract

We prove strong convergence of an iterativescheme for approximation of fixed point of $\lambda$-strictpseudocontractive mapping in a uniformly smooth real Banach space(which is not necessarily uniformly convex). We apply our resultto approximation of common fixed point of a finite family ofstrictly pseudocontractive mappings. Our result extends theresults of Li and Yao [M. Li, Y. Yao, Strong convergence of aniterative algorithm for $\lambda$-strictly pseudocontractivemappings in Hilbert spaces, An. St. Univ. Ovidius Constanta 18(2010), 219-228] and complements other new interesting results inthe literature.