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Certain radii problems for 𝓢∗(ψ) and special functions

  • Kamaljeet Gangania EMAIL logo and S. Sivaprasad Kumar
Published/Copyright: May 13, 2024
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Abstract

In Geometric function theory, the Ma-Minda class of starlike functions has a unique place as it unifies various subclasses of starlike functions. There has been an vivid interplay between special functions and their geometric properties, like starlikeness. In this article, we establish certain special function’s radius of Ma-Minda starlikness. As an application, we obtain conditions on parameters for these special functions to be in the Ma-Minda class. Further, we focus on certain convolution properties for the Ma-Minda class that are not done so far, and study their applications in radius problem. Finally, we prove a variational problem of Goluzin, namely, the region of variability for the Ma-Minda class. Our results simplify and generalize the already-known ones.

Acknowledgement

The authors would like to thank the editor and anonymous referees for their insightful comments to improve the earlier version of the article.

  1. (Communicated by Stanisława Kanas)

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Received: 2023-01-17
Accepted: 2023-03-23
Published Online: 2024-05-13
Published in Print: 2024-02-26

Š 2024 Mathematical Institute Slovak Academy of Sciences

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