Mean p-angular distance orthogonality in normed linear spaces

Abstract

In this paper, we introduce and study a new concept of orthogonality, namely, mean p-angular distance orthogonality in normed linear spaces. We investigate main properties of this type of orthogonality and its relation to some other previously defined generalized orthogonalities. Then, we study α-existence, α- diagonal existence and S-existence theorems for this type of orthogonality. Moreover, a new characterization of inner product spaces is given in terms of property (H), properly formulated for the mean p-angular distance orthogonality.