Non-Bazilevič Functions Defined by Generalized M-Series Subordinating With Generalized Telephone Numbers

Compared to the class of Bazilevič functions, the so-called non-Bazilevič functions have not been investigated as thoroughly. A convex combination of the class of non-Bazilevič functions and its Alexander transform characterisation would be used to describe and analyze a new class of functions. The differential operator that is used to define the function class involves generalized M-series. In addition to unifying the generalized Gaussian hypergeometric function and the Mittag-Leffler function, the generalized M-series also generalizes a number of other well-known topics in univalent function theory. We focus on estimates involving the initial coefficients of the functions with Maclaurin series that are part of the defined function class. Additionally, we acquire the inverse and logarithmic coefficients for the specified function class.