Abstract and Applied Analysis

Convergence Theorems for a Maximal Monotone Operator and a V -Strongly Nonexpansive Mapping in a Banach Space

Hiroko Manaka

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Abstract

Let E be a smooth Banach space with a norm . Let V ( x , y ) = x 2 + y 2 2 x , J y for any x , y E , where , stands for the duality pair and J is the normalized duality mapping. With respect to this bifunction V ( , ) , a generalized nonexpansive mapping and a V -strongly nonexpansive mapping are defined in E . In this paper, using the properties of generalized nonexpansive mappings, we prove convergence theorems for common zero points of a maximal monotone operator and a V -strongly nonexpansive mapping.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 189814, 20 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620762

Digital Object Identifier
doi:10.1155/2010/189814

Mathematical Reviews number (MathSciNet)
MR2680413

Zentralblatt MATH identifier
1368.47071

Citation

Manaka, Hiroko. Convergence Theorems for a Maximal Monotone Operator and a $V$ -Strongly Nonexpansive Mapping in a Banach Space. Abstr. Appl. Anal. 2010 (2010), Article ID 189814, 20 pages. doi:10.1155/2010/189814. https://projecteuclid.org/euclid.aaa/1288620762


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