COEFFICIENT BOUNDS FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS


ALTINKAYA Ş. , YALÇIN TOKGÖZ S.

TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS, vol.6, no.2, pp.180-185, 2015 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1016/j.crma.2015.09.003
  • Title of Journal : TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS
  • Page Numbers: pp.180-185
  • Keywords: analytic and univalent functions, bi-univalent functions, Salagean derivative

Abstract

An analytic function f defined on the open unit disk U = {z : vertical bar z vertical bar < 1} is biunivalent if the function f and its inverse f(-1) are univalent in U. Inspired by the recent work of Hamidi et al. [8], we propose to investigate the coefficient estimates for a general class of analytic and bi-univalent functions. Also, we obtain estimates on the coefficients vertical bar a(2)vertical bar, vertical bar a(3)vertical bar and vertical bar a(n)vertical bar for functions in this class. Some earlier results are shown to be special cases of our results.