Strong convergence of modified implicit hybrid S-iteration scheme for finite family of nonexpansive and asymptotically generalized $\Phi$-hemicontractive mappings

Austine Efut Ofem

doi:10.26637/MJM0804/0053

Abstract

n this paper, we consider a modified implicit 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. [17] can be obtained as a special case of our iteration process. Our result mainly improves and extends the result of Kang et al. [17] and several other results in the literation from the class of strongly psudocontractive mapping to the more general class asymptotically generalized $\Phi$-hemicontractive mappings. A different approach is used to obtain our result and the necessity of applying condition (C3) for the two mappings is weaken to only one mapping.

Keywords:

Fixed point, Banach space, Implicit hybrid S-iteration process, nonexpansive mapping, asymptotically generalized F-hemicontractive mapping.

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Austine Efut Ofem Department of Mathematics, University of Uyo, Uyo, Nigeria. https://orcid.org/0000-0001-8064-2326

Pages: 1643-1649
Date Published: 01-01-2020
Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

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