Growth and distortion theorem for the Janowski alpha-spirallike functions in the unit disc

Polatoglu Y.

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, no.2, pp.255-259, 2012 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2012
  • Journal Name: STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.255-259
  • Istanbul Kültür University Affiliated: Yes

Abstract

Let A be the class of all analytic functions in the open unit disc D = {z vertical bar vertical bar z vertical bar < 1} of the form f(z) = z + a(2)z(2) + a(3)z(3) + .... Let g(z) be an element of A satisfying the condition ei alpha g'(z)/g(z) = 1 + A phi(z)/1 + B phi(z) where vertical bar alpha vertical bar < pi/2, -1 <= B < A <= 1 and phi(z) is analytic in D and satisfies the conditions phi(0) = 0, vertical bar phi(z)vertical bar < 1 for every z is an element of D. Then g(z) is called Janowski alpha-spirallike functions in the unit disc. The class of such functions is denoted by S-alpha*(A,B). The aim of this paper is to give growth and distortion theorems for the class S-alpha*(A, B).