Some results of the class of functions with bounded radius rotation

Polatoglu Y., Kahramaner Y., Şen Y.

Journal of Computational Analysis and Applications, vol.26, no.6, pp.1006-1013, 2019 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 6
  • Publication Date: 2019
  • Journal Name: Journal of Computational Analysis and Applications
  • Journal Indexes: Scopus
  • Page Numbers: pp.1006-1013
  • Keywords: Bounded boundary rotation, Bounded radius rotation, Distortion theorem, Growth theorem and coefficient inequality
  • Istanbul Kültür University Affiliated: Yes

Abstract

Let A be the family of functions f(z) = z + a2z2+ which are analytic in the open unit disc 𝔻 = {z: |z| < 1}, and denote by P of functions p(z) = z + p1z + p2z2 + analytic in 𝔻 such that p(z) is in P if and only if (Formula presented) for some Schwarz function ϕ-(z) and every z ∈ 𝔻: Let f(z) be an element of A, and satisfies the condition (Formula presented) where p1(z); p2(z) ∈ P and k ≥ 2, then f(z) is called function with bounded radius rotation. The class of such functions is denoted by Rk. This class is generalization of starlike functions. The main purpose is to give some properties of the class Rk.