Strong convergence of modified implicit hybrid S-iteration scheme for finite family of nonexpansive and asymptotically generalized \(\Phi\)-hemicontractive mappings
Austine Efut Ofem · Malaya Journal of Matematik · 2020
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.