Path Convergence and Approximation of Common Zeroes of a Finite Family of -Accretive Mappings in Banach SpacesReport as inadecuate




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Abstract and Applied AnalysisVolume 2010 2010, Article ID 285376, 14 pages

Research Article

Department of Mathematics, University of Nigeria, Nsukka, Nigeria

Mathematics Institute, African University of Science and Technology, Abuja, Nigeria

Received 29 January 2010; Revised 19 June 2010; Accepted 27 June 2010

Academic Editor: S. Reich

Copyright © 2010 Yekini Shehu and Jerry N. Ezeora. 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.

Abstract

Let be a real Banach space which is uniformly smooth and uniformly convex. Let be anonempty, closed, and convex sunny nonexpansive retract of , where is the sunny nonexpansive retraction. If admits weakly sequentially continuous duality mapping , path convergence is proved for a nonexpansivemapping . As an application, we prove strong convergence theorem for common zeroes of a finitefamily of -accretive mappings of to . As a consequence, an iterative scheme is constructed to converge toa common fixed point assuming existence of a finite family of pseudocontractive mappings from to under certain mild conditions.





Author: Yekini Shehu and Jerry N. Ezeora

Source: https://www.hindawi.com/



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