Modified S iteration process for total asymptotically nonexpansive mappings in hyperbolic spaces

Samir Dashputre

Abstract


This paper provides a fixed point theorem and iterative construction of a fixed point for a general class of nonlinear mapping in the setup of uniformly convex hyperbolic spaces. We translate modified $S$-iteration process, essentially  due to Agarwal, O'Regan and Sahu \cite{ag} in such setting for approximation of fixed points of a total asymptotically nonexpansive mappings.  As a consequence, we establish strong and $\Delta$-convergence results which extend and generalize various corresponding results in uniformly convex Banach spaces and CAT(0) spaces announced in the current literature (see e.g.,  \cite{ fu1, fu2, kh, kh2, ki3, wan, zhao} in the sense  of faster iteration process.

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|ISSN 1686-0209|