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 $\alpha$-existence‎, ‎$\alpha$-diagonal existence and S-existence theorems for this type of orthogonality‎. ‎Moreover‎, ‎a new characterization of inner product spaces is given based on the mean p-angular distance orthogonality‎.