Certain subclass of Meromorphic function associated with Wright function

TL;DR

This paper introduces a new subclass of meromorphic functions linked with Wright functions, deriving integral representations, coefficient estimates, and geometric properties like starlikeness and convexity.

Contribution

It defines the class $\Sigma( heta, \lambda, \gamma)$ using a Wright function-based operator and establishes new integral, convolution, and coefficient bounds.

Findings

Derived exact integral representation for the class

Established coefficient estimates for functions in the class

Determined radii of meromorphic starlikeness and convexity

Abstract

In this paper, we introduce and investigate a novel subclass $\Sigma(\theta, \lambda, \gamma)$ of meromorphic functions defined in the punctured unit disk ${D}^*$. This class is constructed utilizing a specialized generalized operator $W_{\alpha, \beta}$ associated with Wright function. We derive the exact integral representation and establish necessary and sufficient convolution (Hadamard product) conditions. Furthermore, sufficient conditions involving strict inequalities are provided for functions to be members of this class $\Sigma(\theta, \lambda, \gamma)$. Additionaly, by employing the properties of Carath\'eodory functions and the principle of mathematical induction, we establish coefficient estimates for functions belonging to this new class. Finally, as an applications, we the established coefficient bounds, we determine the precise radii of meromorphic starlikeness and meromorphic convexity of order $\rho$. The results presented in this study generalize several existing outcomes in geometric Function Theory.