Characterization of <i>p</i> -valent <i>q</i> -starlike functions through Hadamard product and Poisson distribution

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 (|z| &lt;1). 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.