Approximation of common fixed points of finite family of nonexpansive and asymptotically generalized $\Phi$--hemicontractive mappings

Abstract

In this paper, we propose a modified hybrid S-iteration scheme for finite family of nonexpansive and asymptotically generalized $\Phi$--hemicontractive mappings in the frame work of real Banach spaces. We remark that the iteration process of Kang et al. \cite{Kang1} can be obtained as a special case of our iteration process. A different approach is used to obtain our result and the necessity of condition (C3) is not required to prove our strong convergence theorem. Our result mainly extends and complements the result of \cite{Kang1} and several other related results in the literature.