A class of p-valent functions of complex order is defined with the primary motive of unifying the concept of prestarlike functions with various other classes of multivalent functions. Interesting properties such as inclusion relations, integral representation, coefficient estimates and the solution to the Fekete–Szegő problem are obtained for the defined function class. Further, we extended the results using quantum calculus. Several consequences of our main results are pointed out.

We introduce a new class of Bazilevič functions involving the Srivastava–Tomovski generalization of the Mittag-Leffler function. The family of functions introduced here is superordinated by a conic domain, which is impacted by the Janowski function. We obtain coefficient estimates and subordination conditions for starlikeness and Fekete–Szegö functional for functions belonging to the class.

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.