2 = X x X of normed spaces. p- norms and p-HH norms induce the same topology, so they are equivalent, but are geometrically different. Besides that, E. Kikianty and S. S. Dragimor introduced HH-P orthogonality and HH-I orthogonality by using 2-HH norm and discussed main properties of these orthogonalities. The main purpose of this paper is to focus on the concept of 2-HH norm to Birkhoff and a new orthogonality in normed spaces, and we discuss some properties of these orthogonalities. It is proved that Robert orthogonality via 2-HH norm implies Birkhoff-James orthogonality via 2-HH norm; however, it is not necessary for the converse part.
">For any normed space X, the p-HH norms X were introduced by Kikianty and Dragomir on X2 = X x X of normed spaces. p- norms and p-HH norms induce the same topology, so they are equivalent, but are geometrically different. Besides that, E. Kikianty and S. S. Dragimor introduced HH-P orthogonality and HH-I orthogonality by using 2-HH norm and discussed main properties of these orthogonalities. The main purpose of this paper is to focus on the concept of 2-HH norm to Birkhoff and a new orthogonality in normed spaces, and we discuss some properties of these orthogonalities. It is proved that Robert orthogonality via 2-HH norm implies Birkhoff-James orthogonality via 2-HH norm; however, it is not necessary for the converse part.