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

Let E be a smooth Banach space with a norm . Let for any , where stands for the duality pair and J is the normalized duality mapping. With respect to this bifunction , a generalized nonexpansive mapping and a -strongly nonexpansive mapping are defined in . In this paper, using the properties of gene...

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Bibliographic Details
Published in:Abstract and applied analysis 2010, Vol.2010, p.1-20
Main Author: Manaka, Hiroko
Format: Article
Language:English
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Summary:Let E be a smooth Banach space with a norm . Let for any , where stands for the duality pair and J is the normalized duality mapping. With respect to this bifunction , a generalized nonexpansive mapping and a -strongly nonexpansive mapping are defined in . 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 -strongly nonexpansive mapping.
ISSN:1085-3375
1687-0409
DOI:10.1155/2010/189814