Radius of starlikeness of certain analytic functions

Abstract

Abstract This paper studies analytic functions f defined on the open unit disk of the complex plane for which f / g and (1 + z ) g / z are both functions with positive real part for some analytic function g . We determine radius constants of these functions to belong to classes of strong starlike functions, starlike functions of order α , parabolic starlike functions, as well as to the classes of starlike functions associated with lemniscate of Bernoulli, cardioid, lune, reverse lemniscate, sine function, exponential function and a particular rational function. The results obtained are sharp.

Topics & Concepts