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A RANGE PROPERTY RELATED TO NON-EXPANSIVE OPERATORS
Published online by Cambridge University Press: 06 August 2013
Abstract
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In this paper, we prove that if 
$X$ is an infinite-dimensional real Hilbert space and 
$J: X\rightarrow \mathbb{R} $ is a sequentially weakly lower semicontinuous 
${C}^{1} $ functional whose Gâteaux derivative is non-expansive, then there exists a closed ball 
$B$ in 
$X$ such that 
$(\mathrm{id} + {J}^{\prime } )(B)$ intersects every convex and dense subset of 
$X$.
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- Copyright © University College London 2013
References
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