Banach Journal of Mathematical Analysis

Some remarks on the triangle inequality for norms

Lech Maligranda

Full-text: Open access

Abstract

Remarks about strengthening of the triangle inequality and its reverse inequality in normed spaces for two and more elements are collected. There is also a discussion on Fischer-Muszely equality for n-elements in a normed space. Some other estimates which follow from the triangle inequality are also presented.

Article information

Source
Banach J. Math. Anal. Volume 2, Number 2 (2008), 31-41.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336290

Digital Object Identifier
doi:10.15352/bjma/1240336290

Mathematical Reviews number (MathSciNet)
MR2404101

Zentralblatt MATH identifier
1147.46020

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B99: None of the above, but in this section 51M16: Inequalities and extremum problems {For convex problems, see 52A40}

Keywords
inequalities normed space norm inequality triangle inequality reversed triangle inequality angular distance Fischer-Muszely equality

Citation

Maligranda, Lech. Some remarks on the triangle inequality for norms. Banach J. Math. Anal. 2 (2008), no. 2, 31--41. doi:10.15352/bjma/1240336290. https://projecteuclid.org/euclid.bjma/1240336290


Export citation