Starlikeness and convexity of generalized bessel functions

Árpád Baricz, Saminathan Ponnusamy

Research output: Contribution to journalArticle

62 Citations (Scopus)

Abstract

In this paper, we give sufficient conditions for the parameters of the normalized form of the generalized Bessel functions to be convex and starlike in the open unit disk. As an application of our main results, we solve a recent open problem concerning a subordination property of Bessel functions with different parameters. Moreover, we present a new inequality for the Euler gamma function, which we apply in order to have tight bounds for the generalized and normalized Bessel function of the first kind.

Original languageEnglish
Pages (from-to)641-653
Number of pages13
JournalIntegral Transforms and Special Functions
Volume21
Issue number9
DOIs
Publication statusPublished - Aug 13 2010

Keywords

  • Convex functions
  • Gamma function
  • Generalized Bessel functions
  • Starlike functions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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