Classes of multivalent functions analogous to certain classes of univalent starlike functions are defined and studied. Estimates on coefficients and distortion are made, using a variety of techniques. 1. Let St denote the class of all functions/(z) = z + . . . analytic, univalent and starlike in the unit disc U. Such functions satisfy the condition Re(z/'(z)//(z)) >0,zGU. The problem of definin...

Using the derivative operators’ q-analogs values, a wide variety of holomorphic function subclasses, q-starlike, and q-convex functions have been researched examined. With aid fundamental ideas from theory q-calculus operators, we describe new q-operators harmonic Hϱ,χ;qγF(ϖ) in this work. We also define subclass related to Janowski q-analog Le Roy-type Mittag–Leffler functions. Several importa...

These are normalized functions regular and univalent in E: IzI < 1, for which f( E) is starlike with respect to the origin. Let y be a circle contained in E and let [ be the center of y. The Pinchuk question is this: Iff(z) is in ST, is it true thatf(y) is a closed curve that is starlike with respect tof(i)? In Section 5 we will see that the answer is no. There seems to be no reason to demand t...