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Radii of starlikeness of some special functions


Authors: Árpád Baricz, Dimitar K. Dimitrov, Halit Orhan and Nihat Yağmur
Journal: Proc. Amer. Math. Soc. 144 (2016), 3355-3367
MSC (2010): Primary 30C45, 30C15
Published electronically: April 14, 2016
MathSciNet review: 3503704
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Abstract: Geometric properties of the classical Lommel and Struve functions, both of the first kind, are studied. For each of them, three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. For each of the six functions we determine the radius of starlikeness precisely.


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Árpád Baricz
Affiliation: Department of Economics, Babeş-Bolyai University, Cluj-Napoca 400591, Romania — and — Institute of Applied Mathematics, Óbuda University, Budapest 1034, Hungary
Email: bariczocsi@yahoo.com

Dimitar K. Dimitrov
Affiliation: Departamento de Matemática Aplicada, IBILCE, Universidade Estadual Paulista UNESP, São José do Rio Preto 15054, Brazil
Email: dimitrov@ibilce.unesp.br

Halit Orhan
Affiliation: Department of Mathematics, Faculty of Science, Atatürk University, Erzurum 25240, Turkey
Email: horhan@atauni.edu.tr

Nihat Yağmur
Affiliation: Department of Mathematics, Faculty of Arts and Science, Erzincan University, Erzincan 24000, Turkey
Email: nhtyagmur@gmail.com

DOI: https://doi.org/10.1090/proc/13120
Keywords: Lommel functions of the first kind, Struve functions, univalent, starlike functions, radius of starlikeness, zeros of Lommel functions of the first kind, zeros of Struve functions, trigonometric integrals.
Received by editor(s): May 29, 2014
Published electronically: April 14, 2016
Additional Notes: The research of the first author was supported by the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, under Grant PN-II-RU-TE-2012-3-0190. The research of the second author was supported by the Brazilian foundations CNPq under Grant 307183/2013–0 and FAPESP under Grants 2009/13832–9. The research of the third and fourth authors was supported by Erzincan University Rectorship under “The Scientific and Research Project of Erzincan University”, project no. FEN-A-240215-0126.
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society