Birkhoff Orthogonality and Different Particular Cases of Carlsson's Orthogonality on Normed Linear Spaces

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

“…Let X be the normed linear space which we consider to be real. For any x, y ∈ X, 2-HH-N denotesx as the orthogonal toy via the 2-HH norm, which we defined with the help of the new special case of the Carlsson orthogonality discussed in [11]. The Pythagorean orthogonality plays an important role in describing new orthogonality through the medium of the 2-HH norm.…”

“…We introduced a new special case of the Carlsson orthogonality which satisfies all requirements as stated in Carlsson's orthogonality as well as the nondegeneracy, simplification, and continuity property of the inner product space. Furthermore, we proved that such orthogonality is homogeneous if and only if the underlying space is an inner product space [11]. Motivated by the results of Kikianty and Dragomir, and our previous result, we have attempted to introduce a new notion of orthogonality through the medium of the 2-HH norm, which we denote by the 2-HH-N orthogonality.…”