On uniqueness of new orthogonality via 2-HH norm in normed linear space (Q2220228)

Summary: 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 [\textit{S.~S. Dragomir} and \textit{E.~Kikianty}, J. Geom. 98, No.~1--2, 33--49 (2010; Zbl 1210.46014)] 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.