Another approach to characterizations of generalized triangle inequalities in normed spaces

Izumida, Tamotsu; Mitani, Ken-Ichi; Saito, Kichi-Suke

doi:10.2478/s11533-014-0432-z

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2018

2023

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Cited by 2 publications

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“…The author in [7], obtained an alternative way of proving triangle inequality in Banach space. In [8], the authors applied the ψ− sum of the vector points in the Banach space to construct the triangle inequality. The authors in [9], observed that for any vectors (µ 1 , µ 2 , .…”

Section: Introductionmentioning

confidence: 99%

The Proofs of Triangle Inequality Using Binomial Inequalities

Barnes

Wusu-Ansah²,

Amponsah³

et al. 2018

Eur. J. Pure Appl. Math.

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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.

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Section: Introductionmentioning

confidence: 99%