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

Austine Efut Ofem 1*

doi:10.26637/MJM0804/0053

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

Authors :

Austine Efut Ofem ^1*

Author Address :

¹Department of Mathematics, University of Uyo, Uyo, Nigeria.

Abstract :

In 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. \cite{Kang2} can be obtained as a special case of our iteration process. Our result mainly improves and extends the result of Kang et al. \cite{Kang2} 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 $\Phi$-hemicontractive mapping.

DOI :

10.26637/MJM0804/0053

Article Info :

Received : March 24, 2020; Accepted : September 11, 2020.