Journal of Mathematics (Jan 2021)

Starlikeness of Analytic Functions with Subordinate Ratios

  • Rosihan M. Ali,
  • Vaithiyanathan Ravichandran,
  • Kanika Sharma

DOI
https://doi.org/10.1155/2021/8373209
Journal volume & issue
Vol. 2021

Abstract

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Let h be a nonvanishing analytic function in the open unit disc with h0=1. Consider the class consisting of normalized analytic functions f whose ratios fz/gz, gz/zpz, and pz are each subordinate to h for some analytic functions g and p. The radius of starlikeness of order α is obtained for this class when h is chosen to be either hz=1+z or hz=ez. Further, starlikeness radii are also obtained for each of these two classes, which include the radius of Janowski starlikeness, and the radius of parabolic starlikeness.