A generalization of the parallelogram equality in normed spaces
type: Item
instance of: scholarly article
title: A generalization of the parallelogram equality in normed spaces
zbMATH Open document ID: 0933.46020
author: Pavle M. Miličić
published in: Journal of Mathematics of Kyoto University
publication date: 2000-03-29T00:00:00Z
review text: A normed space \(X\) is called quasi-inner product space, if for \(x,y\in X\), \[ \|x+y\|^4-\|x-y\|^4= 8\|x\|^2 g(x,y)+ 8\|y\|^2 g(y,x), \] holds, where \[ g(x,y)= {\|x\|\over 2} \Biggl[\lim_{t\to 0_-} {\|x+ty\|-\|x\|\over t}+ \lim_{t\to 0_+} {\|x+ ty\|-\|x\|\over t}\Biggr]. \] The author proves: A quasi-inner product space is very smooth.
reviewed by: Ismat Beg
Mathematics Subject Classification ID: 46C50
Mathematics Subject Classification ID: 46C15
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 1295042
zbMATH Keywords: parallelogram equality
zbMATH Keywords: smooth space
zbMATH Keywords: quasi-inner product space
zbMATH Keywords: very smooth
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518160
OpenAlex ID: W1959961974
DOI: 10.1215/KJM/1250518160
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description: scientific article; zbMATH DE number 1295042