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

Hiroko Manaka

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: Let E be a smooth Banach space with a norm ∥·∥. Let V(x, y) = ∥x∥2 + ∥y∥2 − 2〈x, Jy〉 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.

Date: 2010
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https://doi.org/10.1155/2010/189814

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:189814

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