New distortion theorems for Sakaguchi functions

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Caglar M., Polatoglu Y.

MATHEMATICAL INEQUALITIES & APPLICATIONS, vol.10, no.4, pp.869-874, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 4
  • Publication Date: 2007
  • Doi Number: 10.7153/mia-10-79
  • Journal Name: MATHEMATICAL INEQUALITIES & APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.869-874
  • Istanbul Kültür University Affiliated: Yes

Abstract

Let A be the class of functions f (z) of the form f (z) = z + Sigma(infinity)(k=2), a(k)z(k) that are analytic in the open unit disk D = {(z) epsilon C | |z| < 1} in 1959, K. Sakaguchi [9] has considered the subclass of A consisting of those f (z) which satisfy Re (zf,(z)/f(z)-f(-z)) > 0, where z E D. We call such a function a "Sakaguchi function", and denote the class of those functions by Ss. Various authors have studied this class ([6, 7, 9, 10]). We obtain new distortion theorems, Koebe domain, k-quasiconformatity, and the radius of convexity for the class S-s.