Open Access

Strong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces

Fixed Point Theory and Applications20072007:059262

DOI: 10.1155/2007/59262

Received: 9 March 2007

Accepted: 12 September 2007

Published: 25 October 2007


Let be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping from to , a nonempty closed convex subset of which is also a sunny nonexpansive retract of , and a non-expansive nonself-mapping with . In this paper, we study the strong convergence of two sequences generated by and for all , where , is a real sequence in an interval , and is a sunny non-expansive retraction of onto . We prove that and converge strongly to and , respectively, as , where is a sunny non-expansive retraction of onto . The results presented in this paper generalize, extend, and improve the corresponding results of Matsushita and Kuroiwa and many others.


Authors’ Affiliations

Department of Mathematics, Faculty of Science, Naresuan University


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© Rabian Wangkeeree. 2007

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