Certain novel generalized subclasses of uniformly starlike and convex functions: coefficient characterizations and inclusion properties through Bessel and Gaussian hypergeometric functions

In this scholarly article, we present novel generalized subclasses of $\nu$ uniformly starlike functions of order $\rho$, designated as $M(\tau ,\rho ,\nu )$, alongside $\nu$ uniformly convex functions of order $\rho$, referred to as $N(\tau ,\rho ,\nu )$. We provide comprehensive coefficient characterizations that delineate the conditions under which analytic functions are classified within the newly established subclasses of uniformly starlike and uniformly convex families, respectively. Furthermore, we conduct an analysis of the implications of the Bessel function and explore the consequences of the Gaussian hypergeometric function on these mathematical classes to substantiate an inclusion property for analytic functions that reside within these subclasses.