On Uniqueness of New Orthogonality via 2-HH Norm in Normed Linear Space. (21st November 2020)

• Record Type: Journal Article
• Authors: Ojha, Bhuwan Prasad; Bajracharya, Prakash Muni; Mishra, Vishnu Narayan
• Other Names: Mohiuddine Syed Abdul Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-11-21
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/8835492
• Languages: English
• ISSNs: 2314-8896

Abstract

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.