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Geometric properties of functions containing derivatives of Bessel function

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Abstract

Let \(J_\xi (z)\) denotes the Bessel function of the first kind of order \(\xi .\) For three different kinds of normalizations of \(N_\xi (z)=az^2J_\xi ^{\prime \prime }(z)+bzJ_\xi ^{\prime }(z)+cJ_\xi (z)\), we find the radius for Ma–Minda classes: \(\mathcal {S}^*\left( \varphi \right)\)-radii and \(\mathcal {C}\left( \varphi \right)\)-radii. We further establish the radii of \(\gamma\)-spirallike of order \(\alpha\) and convex \(\gamma\)-spirallike of order \(\alpha\) of these normalized functions. As an application of our results, we derive sufficient conditions for the \(N_\xi (z)\) to be a member of the unified subclasses of starlike and convex functions. The obtained radii are sharp.

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Authors and Affiliations

  1. Institute of Innovation in Technology and Management, New Delhi, 110058, India

    Kamaljeet Gangania

  2. Department of Mathematics, Faculty of Science and Literature, Kafkas University, Campus, 36100, Kars, Turkey

    Sercan Kazımoğlu

Authors
  1. Kamaljeet Gangania
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  2. Sercan Kazımoğlu
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All authors contributed equally.

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Correspondence to Kamaljeet Gangania.

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Communicated by Arpad Baricz.

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Gangania, K., Kazımoğlu, S. Geometric properties of functions containing derivatives of Bessel function. J Anal (2024). https://doi.org/10.1007/s41478-024-00737-0

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