Differential inequalities and Bessel functions

Árpád Baricz, Saminathan Ponnusamy

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let S(α,β,λ) denote the class of analytic functions f defined on the unit disk D with the normalization f(0)=f'(0)-1=0, z/f(z)≠0 in D and satisfy the condition {pipe}f'(z)(zf(z))2-βz3(zf(z))‴-(α+β)z2(zf(z))″-1{pipe}≤λ for all z∈D and for some real constants α>-1 and β such that α+β>-1. We find conditions on constants α>-1 and β such that functions in S(α,β,λ) are univalent in D. As a consequence of our investigation, we present univalence and starlikeness criteria. As applications, we present conditions such that z/up,b,c is in S(α,β,λ), where up,b,c denotes the suitably normalized form of the generalized Bessel functions of the first kind.

Original languageEnglish
Pages (from-to)558-567
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume400
Issue number2
DOIs
Publication statusPublished - Apr 15 2013

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Keywords

  • Analytic, univalent and starlike functions
  • Bessel functions
  • Coefficient inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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