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The Radius of \(\alpha \)-Convexity of Normalized Bessel Functions of the First Kind

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Abstract

The radii of \(\alpha \)-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 \(\alpha \in [0,1]\), and they are decreasing with respect to the parameter \(\alpha \). 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.

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Authors and Affiliations

  1. Department of Economics, Babeş-Bolyai University, 400591, Cluj-Napoca, Romania

    Árpád Baricz

  2. Institute of Applied Mathematics, Óbuda University, Budapest, 1034, Hungary

    Árpád Baricz

  3. Department of Mathematics, Faculty of Science, Atatürk University, 25240, Erzurum, Turkey

    Halit Orhan

  4. Department of Mathematics and Informatics, Sapientia Hungarian University of Transylvania, 540485, Târgu-Mureş, Romania

    Róbert Szász

Authors
  1. Árpád Baricz
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  2. Halit Orhan
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  3. Róbert Szász
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Corresponding author

Correspondence to Árpád Baricz.

Additional information

Communicated by Roger W. Barnard.

The research of Á. Baricz was supported by a research grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-RU-TE-2012-3-0190. The authors wish to acknowledge the referee’s comments and suggestions which enhanced this paper.

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Baricz, Á., Orhan, H. & Szász, R. The Radius of \(\alpha \)-Convexity of Normalized Bessel Functions of the First Kind. Comput. Methods Funct. Theory 16, 93–103 (2016). https://doi.org/10.1007/s40315-015-0123-1

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  • DOI: https://doi.org/10.1007/s40315-015-0123-1

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