A generalized orthogonality relation via norm derivatives in real normed linear spaces

چکیده مقاله

We introduce a generalized orthogonality relation in real normed linear spaces via norm derivatives. The relation between this concept and other types of orthogonalities such as Birkhoff–James orthogonality and orthogonality relations connected with norm derivatives is investigated. As an application, some new characterizations of smooth real normed linear spaces are obtained. Moreover, some mapping theorems with respect to this new type of orthogonality are presented.