Two mappings related to semi-inner products and their applications in geometry of normed linear spaces
type: Item
instance of: scholarly article
title: Two mappings related to semi-inner products and their applications in geometry of normed linear spaces
zbMATH Open document ID: 0996.46007
DOI: 10.1023/A:1022268627299
author: J. J. Koliha
author: Silvestru Sever Dragomir
published in: Applications of Mathematics
publication date: 2002-10-15T00:00:00Z
full work available at URL: https://eudml.org/doc/33064
review text: Two mappings associated with the lower and upper semi-inner products \((\cdot ,\cdot)_i\) and \((\cdot ,\cdot)_s\) and with semi-inner product \([\cdot ,\cdot ]\) (in the sense of Lumer) are introduced. The mappings generate the norm of a real normed linear space. Monotonicity and boundedness of these mappings is studied and it is given a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46C50
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 1814836
zbMATH Keywords: lower and upper semi-inner product
zbMATH Keywords: semi-inner product
zbMATH Keywords: Schwarz inequality
zbMATH Keywords: smooth normed spaces
zbMATH Keywords: Birkhoff orthogonality
zbMATH Keywords: best approximants
MaRDI profile type: Publication
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OpenAlex ID: W1968825347
description: scientific article; zbMATH DE number 1814836