Characterization of p-valent q-starlike functions through Hadamard product and Poisson distribution

Abstract

This paper presents significant advancement in the study of multivalent functions by introducing three new subclasses of p-valent q-starlike functions, defined with respect to higher-order q-derivatives within the open unit disk of the complex plane [Formula: see text]. We utilized the Poisson distribution as a coefficient and applied the Hadmard product to derive several essential properties of these q-starlike functions, including distortion theorems and radius problems, particularly in case with negative coefficients. These findings enhance our understanding of the function behaviour and contribute to the broader mathematical discourse.

Keywords

• Analytic functions
• q-derivative (or q-difference) operator
• q-starlike functions
• passion distribution
• Hadmard product
• Primary 05A30