Geometric Properties of Operators Associated with Normalized Jackson and Hahn-Exton $q$-Bessel Functions and $q$-Extension of the Hohlov Integral Operator
DOI:
https://doi.org/10.52737/18291163-2025.17.15-1-32Keywords:
q-Convex Functions, q-Starlike Functions, q-Hypergeometric Function, q-Bessel FunctionAbstract
In this paper, we examine the geometric properties of linear operators associated with normalized Jackson and Hahn-Exton $q$-Bessel functions that arise through suitable transformations and $q$-extension of the Hohlov integral operator. These operators are investigated in the framework of the function from the class $\mathcal{M}_{\xi,\varkappa}^{\varpi,\theta}(z;q)$. We derive coefficient bounds and sufficient conditions for functions in the class $\mathcal{M}_{\xi,\varkappa}^{\varpi,\theta}(z;q)$. Additionally, we explore inclusion properties by using the Taylor coefficients of $z_2\phi_1(a,b;c;q,z)$ and the normalized Jackson and Hahn-Exton $q$-Bessel functions. The primary objective is to derive sufficient conditions under which the convolution operators will be in different subclasses of $q$-starlike and $q$-convex functions.
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