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Commun. Korean Math. Soc. 2015; 30(3): 209-219
Printed July 31, 2015
https://doi.org/10.4134/CKMS.2015.30.3.209
Copyright © The Korean Mathematical Society.
Strong and $\Delta $-convergence of a faster iteration process in hyperbolic space
Sezgin Akbulut and Birol Gunduz
Ataturk University, Erzincan University
In this article, we first give metric version of an iteration scheme of Agarwal et al.~\cite{Agarwal} and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.
Keywords: hyperbolic space, nonexpansive map, common fixed point, iterative process, condition (A), semi-compactness, $\Delta $-convergence
MSC numbers: Primary 47H09, 47H10, 49M05
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