P-angular distance orthogonality

Abstract

We present a new orthogonality which is based on p-angular distance in normed linear spaces. This orthogonality generalizes the Singer and isosceles orthogonalities to a vast extent. Some important properties of this orthogonality, such as the $$\alpha $$-existence and the $$\alpha $$-diagonal existence, are established with giving some natural bounds for $$\alpha $$. It is shown that a real normed linear space is an inner product space if and only if the p-angular distance orthogonality is either homogeneous or additive. Several examples are presented to illustrate the results.