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2010 NONEXPANSIVE RETRACTIONS ONTO CLOSED CONVEX CONES IN BANACH SPACES
Takashi Honda, Wataru Takahashi, Jen-Chih Yao
Taiwanese J. Math. 14(3B): 1023-1046 (2010). DOI: 10.11650/twjm/1500405903

Abstract

Let $E$ be a smooth, strictly convex and reflexive Banach space, let $C^*$ be a closed convex subset of the dual space $E^*$ of $E$ and let $\Pi_{C^*}$ be the generalized projection of $E^*$ onto $C^*$. Then the mapping $R_{C^*}$ defined by $R_{C^*} = J^{-1} \Pi_{C^*}J$ is a sunny generalized nonexpansive retraction of $E$ onto $J^{-1}C^{*}$, where $J$ is the normalized duality mapping on $E$. In this paper, we first prove that if $K$ is a closed convex cone in $E$ and $P$ is the nonexpansive retaction of $E$ onto $K$, then $P$ a sunny generalized nonexpansive retraction of $E$ onto $K$. Using this result, we obtain an equivalent condition for a closed half-space of $E$ to be a nonexpansive retract of $E$.

Citation

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Takashi Honda. Wataru Takahashi. Jen-Chih Yao. "NONEXPANSIVE RETRACTIONS ONTO CLOSED CONVEX CONES IN BANACH SPACES." Taiwanese J. Math. 14 (3B) 1023 - 1046, 2010. https://doi.org/10.11650/twjm/1500405903

Information

Published: 2010
First available in Project Euclid: 18 July 2017

zbMATH: 1231.47055
MathSciNet: MR2674594
Digital Object Identifier: 10.11650/twjm/1500405903

Subjects:
Primary: 47H09
Secondary: 47H10, 60G05

Rights: Copyright © 2010 The Mathematical Society of the Republic of China

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Vol.14 • No. 3B • 2010
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