Characterization of a generalized triangle inequality in normed spaces

Dadipour, Farzad; Moslehian, Mohammad Sal; Rassias, John Michael; Takahasi, Sin–Ei

doi:10.1016/j.na.2011.09.004

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction4

Approximately Bisectrix-orthogonality Preserving Mappings1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2012

2023

Publication Types

Select...

Article7

Other1

Relationship

Self Cite0

Independent8

Authors

Journals

Cited by 12 publications

(5 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The next lemma plays an essential role in our work. It provides indeed a reverse of the triangle inequality; see [8].…”

Section: Approximately Bisectrix-orthogonality Preserving Mappingsmentioning

confidence: 96%

Approximately bisectrix-orthogonality preserving mappings

Zamani

2014

commath

View full text Add to dashboard Cite

show abstract

“…The next lemma plays an essential role in our work. It provides indeed a reverse of the triangle inequality; see [8].…”

Section: Approximately Bisectrix-orthogonality Preserving Mappingsmentioning

confidence: 96%

Approximately bisectrix-orthogonality preserving mappings

Zamani

2014

commath

View full text Add to dashboard Cite

show abstract

“…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.

View full text Add to dashboard Cite

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.

show abstract

“…Another extension of Maligranda’s inequality for n elements in a Banach space was obtained in Mitani and Saito [7]. The problem of characterization of all intermediate values C satisfying , for in a Banach space is studied by Mineno, Nakamura and Ohwada [8], Dadipour et al [9], Sano et al [10] and others. For other different results about the triangle inequality we mention only [11–15].…”

Section: Introductionmentioning

confidence: 99%