Geometric Properties of Generalized Bessel Functions

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The goal of the present chapter is to study some geometric properties (like univalence, starlikeness, convexity, close-to-convexity) of generalized Bessel functions of the first kind. In order to achieve our goal we use several methods: differential subordinations technique, Alexander transform, results of L. Fejér, W. Kaplan, S. Owa and H.M. Srivastava, S. Ozaki, S. Ponnusamy and M. Vuorinen, H. Silverman, and Jack’s lemma. Moreover, we present some immediate applications of univalence and convexity involving generalized Bessel functions associated with the Hardy space and a monotonicity property of generalized and normalized Bessel functions of the first kind.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages23-69
Number of pages47
DOIs
Publication statusPublished - Jan 1 2010

Publication series

NameLecture Notes in Mathematics
Volume1994
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

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Keywords

  • Analytic Function
  • Bessel Function
  • Convex Function
  • Geometric Property
  • Unit Disk

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Baricz, A. (2010). Geometric Properties of Generalized Bessel Functions. In Lecture Notes in Mathematics (pp. 23-69). (Lecture Notes in Mathematics; Vol. 1994). Springer Verlag. https://doi.org/10.1007/978-3-642-12230-9_2