The mapping δx,y in normed linear spaces and refinements of the Cauchy-Schwarz inequality

被引：2

作者：

Dragomir, SS

Koliha, JJ ^{[1
]}

机构：

[1] Univ Melbourne, Dept Math & Stat, Parkville, Vic 3052, Australia

[2] Univ Transkei, Dept Math, ZA-5100 Unitra, Umtata, South Africa

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2000年 / 41卷 / 1-2期

关键词：

normed linear spaces; the lower and upper semi-inner product; inner product spaces; the Cauchy-Schwarz inequality;

D O I：

10.1016/S0362-546X(98)00274-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The mapping δx,y(t) = 2∥x+ty∥-∥x+2ty∥, which arises naturally in geometric arguments on normed spaces which use the lower and upper semi-inner product as defined is introduced. The properties of monotonicity, boundedness and convexity of this mapping are studied. Applications to inequalities in analysis, including refinements of the Cauchy-Schwarz inequality, both in normed linear and inner products spaces are presented.

引用

页码：205 / 220

页数：16

共 11 条

[1] Inequalities related to the Cauchy-Schwarz inequality
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[9] An orthogonality in normed linear spaces based on angular distance inequality
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