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

Mfon O. Udo

doi:10.26637/mjm0903/002

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.

Keywords:

Fixed point, Banach space, hybrid $S$-iteration process, nonexpansive mapping, asymptotically generalized $\Phi$-hemicontractive mapping

Mathematics Subject Classification:

53C40 , 53C50

Authors Imprint References Funding Related Articles Downloads

Mfon O. Udo Department of Mathematics, Akwa Ibom state University, Ikot Akpaden, Nigeria.

Pages: 72-82
Date Published: 01-07-2021
Vol. 9 No. 03 (2021): Malaya Journal of Matematik (MJM)

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