Abstract and Applied Analysis

Path Convergence and Approximation of Common Zeroes of a Finite Family of m -Accretive Mappings in Banach Spaces

Yekini Shehu and Jerry N. Ezeora

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Abstract

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

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 285376, 14 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620757

Digital Object Identifier
doi:10.1155/2010/285376

Mathematical Reviews number (MathSciNet)
MR2674393

Zentralblatt MATH identifier
1206.47086

Citation

Shehu, Yekini; Ezeora, Jerry N. Path Convergence and Approximation of Common Zeroes of a Finite Family of $m$ -Accretive Mappings in Banach Spaces. Abstr. Appl. Anal. 2010 (2010), Article ID 285376, 14 pages. doi:10.1155/2010/285376. https://projecteuclid.org/euclid.aaa/1288620757


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