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|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
|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
|Description: ||This article is published in EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS|
|Appears in Collections:||College of Science|
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