A Comprehensive Class Of Starlike Functions Involving Mittag-Leffler Function

ABSTRACT

A new class of Bazilevič functions of the type κ+iμ is defined involving differential characterizations inspired by the study of multiplicative calculus. The defined function class unifies the studies of well-known subclasses like convex, starlike and alpha-convex functions. To further make our study more versatile, we have studied the new function class involving a differential operator defined using the Mittag-Leffler function. Estimates of Taylor–Maclaurin coefficients a2 and a3 of the functions which belong to the defined function class are obtained. Further, the Fekete–Szeg˝o inequality of this new class which was computationally cumbersome is part of our main results in this paper.