Convergence Theorems of a New Three-Step Iteration for Nonself Asymptotically Nonexpansive Mappings

Birol Gunduz, Sezgin Akbulut

Abstract


Let E be a real uniformly convex and smooth Banach space with P as a sunny nonexpansive retraction, K be a nonempty closed convex subset of E. Let T_{i}:K→E (i=1,2,3) be three of weakly inward and nonself asymptotically nonexpansive mappings with respect to P. It is proved that three step iteration converges weakly and strongly to a common fixed point of T_{i} (i=1,2,3) under certain conditions. It presents some new results in this paper.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|