A RANGE PROPERTY RELATED TO NON-EXPANSIVE OPERATORS. Issue 1 (6th August 2013)

• Record Type: Journal Article
• Authors: Ricceri, Biagio
• Is Part Of: Mathematika. Volume 60:Issue 1(2014)
• Page Start: 232
• Page End: 236
• Publication Date: 2013-08-06
• Subjects: 47H09, -- 47H05, -- 49J35 (primary); Mathematics -- Periodicals; 510.5
• DOI: 10.1112/S0025579313000120
• Languages: English
• ISSNs: 0025-5793

Abstract

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 $X$ .