Estimates for univalent functions

Rabha W. Ibrahim, Maslina Darus

Research output: Contribution to journalArticle

Abstract

For normalized analytic functions f in the open unit disk U:= {z: |z| < 1}, we consider the subclass where 0 ≤ α< 1. In this note, we determined an upper bound of the pre-Schwarzian norm for functions f ∈ S *(α). Furthermore, by using Jack's Lemma, we pose the sufficient conditions for normalized function f to be in S *(α). Subordination relations are introduced.

Original languageEnglish
Pages (from-to)265-272
Number of pages8
JournalInternational Journal of Mathematical Analysis
Volume6
Issue number5-8
Publication statusPublished - 2012

Fingerprint

Univalent Functions
Subordination
Estimate
Unit Disk
Lemma
Analytic function
Upper bound
Norm
Sufficient Conditions

Keywords

  • Analytic function
  • Jack's Lemma
  • Pre-Schwarzian derivative
  • Starlike functions
  • Subordination
  • Superordination
  • Unit disk
  • Univalent functions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Estimates for univalent functions. / Ibrahim, Rabha W.; Darus, Maslina.

In: International Journal of Mathematical Analysis, Vol. 6, No. 5-8, 2012, p. 265-272.

Research output: Contribution to journalArticle

Ibrahim, Rabha W. ; Darus, Maslina. / Estimates for univalent functions. In: International Journal of Mathematical Analysis. 2012 ; Vol. 6, No. 5-8. pp. 265-272.
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