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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/12103

Title: The Proofs of Triangle Inequality Using Binomial Inequalities
Authors: Barnes, Benedict
Owusu-Ansah, E. D. J.
Amponsah, S. K.
Adjei, I. A.
Keywords: Triangle inequality
triangle through binomial inequality
triangle inequality through Euclidean norm
Hilbert space
Issue Date: Jan-2018
Publisher: EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
Citation: EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, Vol. 11, No. 1, 2018, 352-361
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.
Description: This article is published in EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
URI: http://hdl.handle.net/123456789/12103
ISSN: 1307-5543
Appears in Collections:College of Science

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