Two Mappings Related To Semi-Inner Products And Their Applications in Geometry of Normed Linear Spaces

Dragomir, Sever S and Koliha, Jerry J (1998) Two Mappings Related To Semi-Inner Products And Their Applications in Geometry of Normed Linear Spaces. RGMIA research report collection, 2 (1).

Abstract

In this paper we introduce two mappings associated with the lower and upper semiinner product (.,.)i and (.,.)s and with semi-inner products [.,.] (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give 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.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/17128
Subjects Historical > FOR Classification > 0102 Applied Mathematics
Historical > FOR Classification > 0103 Numerical and Computational Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords lower and upper semi-inner product, semi-inner products, Schwarz inequality, smooth normed spaces, Birkhoff orthogonality, best approximants
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