On an inequality of Bynum and Drew
type: Item
instance of: scholarly article
title: On an inequality of Bynum and Drew
zbMATH Open document ID: 0716.46023
DOI: 10.1016/0022-247X(90)90201-P
author: Ryszard Smarzewski
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: For the abstract \(L_ p\) space X with \(1<p\leq 2\) it is proved that for all x,y\(\in X\) and \(0<t<1\) \[ \| (1-t)x+ty\|^ 2\leq (1-t)\| x\|^ 2+t\| y\|^ 2-(p-1)t(1-t)\| x-y\|^ 2. \] This result is applied to show the strong uniqueness of best approximations and existence of fixed points for uniformly Lipschitzian mappings and to prove that if \(J_ s(X)\) is the self-Jung constant [see \textit{D. Amir}, Pac. J. Math. 118, 1-15 (1985; Zbl 0529.46011)] then \(J_ s(X)\leq 2/\sqrt{p}\).
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 4180095
zbMATH Keywords: abstract \(L_ p\) space
zbMATH Keywords: strong uniqueness of best approximations
zbMATH Keywords: existence of fixed points for uniformly Lipschitzian mappings
zbMATH Keywords: self-Jung constant
reviewed by: Fedor Sukochev
MaRDI profile type: Publication
cites work: On Jung's constant and related constants in normed linear spaces
cites work: A Weak Parallelogram Law for l p
cites work: Q4188284
cites work: Strongly unique best approximations and centers in uniformly convex spaces
cites work: Strongly unique minimization of functionals in Banach spaces with applications to theory of approximation and fixed points
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cites work: Asymptotic Chebyshev centers
description: scientific article; zbMATH DE number 4180095