Strong convergence theorems using three-step mean iteration for Zamfirescu mappings in Banach spaces

Abstract

This paper addresses the approximation problem for fixed points of Zamfirescu mappings (Z-mapping) [Arch.  Math. 23(1) (1972), 292-298]. We use a three-step mean iteration that combines Noor's iteration as well as Atsushiba and Takahashi's mean iteration, and we prove a general theorem that extends Berinde's strong convergence theorem [Acta Math. Univ. Comenianae 73 (2004), 119-126]. Our results are obtained in arbitrary real Banach space setting.