Derivatives of generalized farthest functions and existence of generalized farthest points
type: Item
instance of: scholarly article
title: Derivatives of generalized farthest functions and existence of generalized farthest points
zbMATH Open document ID: 1102.46011
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-03-29T00:00:00Z
review text: For a real Banach space \(X\), the relationship between directional derivatives of generalized farthest functions and the existence of generalized farthest points in Banach spaces is investigated. It is proved that a generalized farthest function generated by a bounded closed set having a one-sided directional derivative equal to 1 or~\(-1\) implies the existence of generalized farthest points. New characterization theorems of (compact) locally uniform convex sets are given. This paper continues investigations by F.S.~DeBlasi and J.~Myjak, C.~Li, and R.~Ni.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 5016207
zbMATH Keywords: generalized farthest function
zbMATH Keywords: generalized farthest point
zbMATH Keywords: best approximation
author: Renxing Ni
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.05.005
OpenAlex ID: W2018827715
cites work: Q3810295
cites work: Porous Sets in Best Approximation Theory
cites work: On a generalized best approximation problem
cites work: Geometry of Banach spaces. Selected topics
cites work: Metric projections and the differentiability of distance functions
cites work: Nearest points to closed sets and directional derivatives of distance functions
cites work: On well posed generalized best approximation problems
cites work: On mutually nearest and mutually farthest points in reflexive Banach spaces
cites work: Derivatives of generalized distance functions and existence of generalized nearest points
cites work: On well-posed mutually nearest and mutually furthest point problems in Banach spaces
cites work: Porosity of mutually nearest and mutually furthest points in Banach spaces.
cites work: Ambiguous loci of mutually nearest and mutually furthest points in Banach spaces
cites work: ON ALMOST WELL-POSED MUTUALLY NEAREST AND MUTUALLY FURTHEST POINT PROBLEMS
cites work: Q3154320
cites work: Convex functions, monotone operators and differentiability.
cites work: Q5596489
cites work: The nearest point mapping is single valued nearly everywhere
DOI: 10.1016/J.JMAA.2005.05.005
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description: scientific article; zbMATH DE number 5016207