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A RANGE PROPERTY RELATED TO NON-EXPANSIVE OPERATORS

Part of: Existence theories Nonlinear operators and their properties

Published online by Cambridge University Press:  06 August 2013

Biagio Ricceri
Biagio Ricceri*
Affiliation:
Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy email ricceri@dmi.unict.it
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Abstract

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 $X$.

MSC classification

Secondary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. 47H05: Monotone operators and generalizations 49J35: Minimax problems
Type
Research Article
Information
Mathematika , Volume 60 , Issue 1 , January 2014 , pp. 232 - 236
Copyright
Copyright © University College London 2013 

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References

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