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arXiv · 1906.08319

An application of generalized Bessel functions on subclasses of uniformly spirallike functions

B. A. Frasin·Ibtisam Aldawish
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Abstract

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind $zu_{p}(z)$ to be in the classes $\mathcal{SP}_{p}(\alpha ,\beta )$ and $\mathcal{UCSP}(\alpha ,\beta )$ of uniformly spirallike functions and also give necessary and sufficient conditions for $z(2-u_{p}(z))$ to be in the above classes. Furthermore, we give necessary and sufficient conditions for $\mathcal{I}(\kappa ,c)f$ \ to be in $\mathcal{UCSPT}(\alpha ,\beta )$ provided that the function $f$ is in the class $\mathcal{R}^{\tau }(A,B)$. Finally, we give conditions for the integral operator $\mathcal{G(}\kappa ,c,z\mathcal{)=}% \int_{0}^{z}(2-u_{p}(t))dt$ to be in the class $\mathcal{UCSPT}(\alpha ,\beta ).$ Several corollaries and consequences of the main results are also considered.

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B. A. Frasin, Ibtisam Aldawish. 2019-06-19. An application of generalized Bessel functions on subclasses of uniformly spirallike functions. https://arxiv.org/abs/1906.08319

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