Some Properties of Starlike Functions with Respect to Symmetric-Conjugate Points

Hassoon Al-Amiri, Dan Coman, Petru T. Mocanu

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Let A be the class of all analytic functions in the unit disk U such that f(0) = f'(0) – 1 = 0. A function f G A is called starlike with respect to 2n symmetric-conjugate points if Re zf'(z)/fn(z) > 0 for 2 ∊ U where [formula omitted] ω — exp(2πi/n]. This class is denoted by Sn* and was studied in [1]. A sufficient condition for starlikeness with respect to symmetric-conjugate points is obtained. In addition, images of some subclasses of Sn* under the integral operator I : A→A, I(f) = F where [formula omitted] and (g ∊ A is given are determined.

Original languageEnglish (US)
Pages (from-to)469-474
Number of pages6
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume18
Issue number3
DOIs
StatePublished - Jan 1 1995
Externally publishedYes

Keywords

  • differential subordinations
  • integral operator
  • starlike
  • strongly starlike
  • symmetric-conjugate points
  • α-convex

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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