The Proofs of Triangle Inequality Using Binomial Inequalities

Authors

  • Benedict Barnes KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY
  • E.D J.O. Wusu-Ansah
  • S. K. Amponsah
  • I.A. Adjei

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i1.3165

Keywords:

triangle inequality, binomial inequality, Hilbert space

Abstract

In this paper, we introduce the different ways of proving the triangle inequality ku − vk ≤ kuk + kvk, in the Hilbert space. Thus, we prove this triangle inequality through the binomial inequality and also, prove it through the Euclidean norm. The first generalized procedure for proving the triangle inequality is feasible for any even positive integer n. The second alternative proof of the triangle inequality establishes the Euclidean norm of any two vectors in the Hilbert space.

Author Biography

  • Benedict Barnes, KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY

    MATHEMATICS DEPARTMENT

    LECTURER

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Published

2018-02-14

Issue

Vol. 11 No. 1: (January 2018)

Section

Mathematical Psychology

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How to Cite

The Proofs of Triangle Inequality Using Binomial Inequalities. (2018). European Journal of Pure and Applied Mathematics, 11(1), 352-361. https://doi.org/10.29020/nybg.ejpam.v11i1.3165