On Asymmetrical Derivates of Non-Differentiable Functions

Abstract

Let ƒ ( x ) be a non-differentiable function, i.e. a realvalued continuous function denned on a linear interval which has nowhere a finite or infinite derivative. We shall say that ƒ ( x ) has symmetrical derivates at a point x if the four Dini derivates of ƒ ( x ) at x satisfy the relations and otherwise we shall say that ƒ ( x ) has asymmetrical dérivâtes at x .