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

Austine Efut Ofem
2020 Malaya Journal of Matematik  
In this paper, we consider a modified implicit hybrid S-iteration scheme for finite family of nonexpansive and asymptotically generalized Φ-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 » ... mapping to the more general class asymptotically generalized Φ-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.
doi:10.26637/mjm0804/0053 fatcat:p7vwvvn745esth7euo2kkcjx2i