No CrossRef data available.
Article contents
A RANGE PROPERTY RELATED TO NON-EXPANSIVE OPERATORS
Published online by Cambridge University Press: 06 August 2013
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 
$X$.
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 2013
References
Goebel, K. and Reich, S., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker (New York, 1984).Google Scholar
Minty, G. J., Monotone (nonlinear) operators in Hilbert space. Duke Math. J. 29 (1962), 341–346.Google Scholar
Moreau, J.-J., Proximité et dualité dans un espace hilbertien. Bull. Soc. Math. France 93 (1965), 273–299.Google Scholar
Ricceri, B., The problem of minimizing locally a 
${C}^{2} $ functional around non-critical points is well-posed. Proc. Amer. Math. Soc. 135 (2007), 2187–2191.CrossRefGoogle Scholar
${C}^{2} $ functional around non-critical points is well-posed. Proc. Amer. Math. Soc. 135 (2007), 2187–2191.CrossRefGoogle ScholarRicceri, B., A strict minimax inequality criterion and some of its consequences. Positivity 16 (2012), 455–470.Google Scholar
Zeidler, E., Nonlinear Functional Analysis and its Applications, Vol. III, Springer (New York, 1985).CrossRefGoogle Scholar