Quantitative characterization of the difference between Birkhoff orthogonality and isosceles orthogonality

In this paper we introduce a new geometry constant D(X) to give a quantitative characterization of the difference between Birkhoff orthogonality and isosceles orthogonality. We show that 1 and is the upper and lower bound for D(X), respectively, and characterize the spaces of which D(X) attains the upper and lower bounds. We calculate D(X) when X=(R2,‖⋅‖p) and when X is a symmetric Minkowski plane respectively, we show that when X is a symmetric Minkowski plane D(X)=D(X∗).