On some geometric properties and Hardy class of <em>q</em>-Bessel functions

İbrahim Aktaş; İbrahim Aktaş

doi:10.3934/math.2020203

AIMS Mathematics

2020, Volume 5, Issue 4: 3156-3168. doi: 10.3934/math.2020203

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Research article

On some geometric properties and Hardy class of q-Bessel functions

İbrahim Aktaş ^,

Department of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey University, Yunus Emre Campus, 70100, Karaman-Turkey

Received: 12 December 2019 Accepted: 18 March 2020 Published: 25 March 2020
MSC : 30C45, 33C10

In this paper, we deal with some geometric properties including starlikeness and convexity of order α of Jackson's second and third q-Bessel functions which are natural extensions of classical Bessel function J_ν. In additon, we determine some conditions on the parameters such that Jackson's second and third q-Bessel functions belong to the Hardy space and to the class of bounded analytic functions.
- analytic function,
- convex and starlike functions of order α,
- Hardy space,
- q-Bessel functions
Citation: İbrahim Aktaş. On some geometric properties and Hardy class of q-Bessel functions[J]. AIMS Mathematics, 2020, 5(4): 3156-3168. doi: 10.3934/math.2020203

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Abstract

In this paper, we deal with some geometric properties including starlikeness and convexity of order α of Jackson's second and third q-Bessel functions which are natural extensions of classical Bessel function J_ν. In additon, we determine some conditions on the parameters such that Jackson's second and third q-Bessel functions belong to the Hardy space and to the class of bounded analytic functions.

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