The Radius of (Formula presented.) -Convexity of Normalized Bessel Functions of the First Kind

A. Baricz, Halit Orhan, Róbert Szász

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The radii of (Formula presented.) -convexity are deduced for three different kinds of normalized Bessel functions of the first kind and it is shown that these radii are between the radii of starlikeness and convexity, when (Formula presented.) , and they are decreasing with respect to the parameter (Formula presented.). The results presented in this paper unify some recent results on the radii of starlikeness and convexity for normalized Bessel functions of the first kind. The key tools in the proofs are some interlacing properties of the zeros of some Dini functions and the zeros of Bessel functions of the first kind.

Original languageEnglish
Pages (from-to)93-103
Number of pages11
JournalComputational Methods and Function Theory
Volume16
Issue number1
DOIs
Publication statusPublished - Mar 1 2016

Fingerprint

Bessel function of the first kind
Bessel functions
Convexity
Radius
Starlikeness
Interlacing
Zero

Keywords

  • Bessel functions
  • Convex, starlike and (Formula presented.) -convex functions
  • Zeros of Bessel functions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Theory and Mathematics

Cite this

The Radius of (Formula presented.) -Convexity of Normalized Bessel Functions of the First Kind. / Baricz, A.; Orhan, Halit; Szász, Róbert.

In: Computational Methods and Function Theory, Vol. 16, No. 1, 01.03.2016, p. 93-103.

Research output: Contribution to journalArticle

@article{f3997e4568664b29b9535179f9d93566,
title = "The Radius of (Formula presented.) -Convexity of Normalized Bessel Functions of the First Kind",
abstract = "The radii of (Formula presented.) -convexity are deduced for three different kinds of normalized Bessel functions of the first kind and it is shown that these radii are between the radii of starlikeness and convexity, when (Formula presented.) , and they are decreasing with respect to the parameter (Formula presented.). The results presented in this paper unify some recent results on the radii of starlikeness and convexity for normalized Bessel functions of the first kind. The key tools in the proofs are some interlacing properties of the zeros of some Dini functions and the zeros of Bessel functions of the first kind.",
keywords = "Bessel functions, Convex, starlike and (Formula presented.) -convex functions, Zeros of Bessel functions",
author = "A. Baricz and Halit Orhan and R{\'o}bert Sz{\'a}sz",
year = "2016",
month = "3",
day = "1",
doi = "10.1007/s40315-015-0123-1",
language = "English",
volume = "16",
pages = "93--103",
journal = "Computational Methods and Function Theory",
issn = "1617-9447",
publisher = "Springer Verlag",
number = "1",

}

TY - JOUR

T1 - The Radius of (Formula presented.) -Convexity of Normalized Bessel Functions of the First Kind

AU - Baricz, A.

AU - Orhan, Halit

AU - Szász, Róbert

PY - 2016/3/1

Y1 - 2016/3/1

N2 - The radii of (Formula presented.) -convexity are deduced for three different kinds of normalized Bessel functions of the first kind and it is shown that these radii are between the radii of starlikeness and convexity, when (Formula presented.) , and they are decreasing with respect to the parameter (Formula presented.). The results presented in this paper unify some recent results on the radii of starlikeness and convexity for normalized Bessel functions of the first kind. The key tools in the proofs are some interlacing properties of the zeros of some Dini functions and the zeros of Bessel functions of the first kind.

AB - The radii of (Formula presented.) -convexity are deduced for three different kinds of normalized Bessel functions of the first kind and it is shown that these radii are between the radii of starlikeness and convexity, when (Formula presented.) , and they are decreasing with respect to the parameter (Formula presented.). The results presented in this paper unify some recent results on the radii of starlikeness and convexity for normalized Bessel functions of the first kind. The key tools in the proofs are some interlacing properties of the zeros of some Dini functions and the zeros of Bessel functions of the first kind.

KW - Bessel functions

KW - Convex, starlike and (Formula presented.) -convex functions

KW - Zeros of Bessel functions

UR - http://www.scopus.com/inward/record.url?scp=84958540530&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958540530&partnerID=8YFLogxK

U2 - 10.1007/s40315-015-0123-1

DO - 10.1007/s40315-015-0123-1

M3 - Article

AN - SCOPUS:84958540530

VL - 16

SP - 93

EP - 103

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

SN - 1617-9447

IS - 1

ER -