p-angular distance orthogonality

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 α -existence and the α -diagonal existence, are established with giving some natural bounds for α . 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.