Orthogonality of skew type and characterization of inner product spaces

Abstract In this paper, we investigate the generalization of Hermite-Hadamard-type orthogonality within skew structures. Moslehian and Rassias (Commun Math Anal 8:16–21, 2010) characterized inner product spaces by employing the parallelogram law for skew structures in their research. We introduce the concept of skew orthogonality by integrating the parallelogram law of skew structures with Hermite-Hadamard-type orthogonality and discuss its properties. Finally, we characterize inner product spaces using mappings that preserve skew orthogonality.