## Banach Journal of Mathematical Analysis

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

### Some remarks on the triangle inequality for norms

#### 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