On analytic functions with generalized bounded Mocanu variation

It is well known [28] that a number of important classes of univalent functions (e.g. convex, starlike) are related through their derivatives by functions with positive real part. These functions play an important part in problem from signal theory, in moment problems and in constructing quadrature formulas, see Ronning [97] and the references cited therein for some recent applications. In this chapter, we introduce and consider some new classes of functions by replacing functions with positive real part by certain weighted differences of such functions.