On Uniqueness of New Orthogonality via 2-HH Norm in Normed Linear Space-Reference-Cited by-同舟云学术

On Uniqueness of New Orthogonality via 2-HH Norm in Normed Linear Space

Published:2020-11-20 Issue: Volume:2020 Page:1-6
ISSN:2314-8888
Container-title:Journal of Function Spaces
language:en
Short-container-title:Journal of Function Spaces

Author:

Ojha Bhuwan Prasad¹^ORCID,Bajracharya Prakash Muni¹^ORCID,Mishra Vishnu Narayan²^ORCID

Affiliation:

1. Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu, Nepal

2. Department of Mathematics, Faculty of Science, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh, India

Abstract

This paper generalizes the special case of the Carlsson orthogonality in terms of the 2-HH norm in real normed linear space. Dragomir and Kikianty (2010) proved in their paper that the Pythagorean orthogonality is unique in any normed linear space, and isosceles orthogonality is unique if and only if the space is strictly convex. This paper deals with the complete proof of the uniqueness of the new orthogonality through the medium of the 2-HH norm. We also proved that the Birkhoff and Robert orthogonality via the 2-HH norm are equivalent, whenever the underlying space is a real inner-product space.

Publisher

Hindawi Limited

Subject

Analysis

Link

http://downloads.hindawi.com/journals/jfs/2020/8835492.pdf

Reference13 articles.

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4. Orthogonality in normed linear spaces

5. Orthogonality and characterizations of inner product spaces