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Fixed Point Theory and Applications

, 2007:059262 | Cite as

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

  • Rabian Wangkeeree
Open Access
Research Article

Abstract

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

Keywords

Banach Space Differential Geometry Strong Convergence Computational Biology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Rabian Wangkeeree. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceNaresuan UniversityPhitsanulokThailand

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