Initial Successive coefficients of Inverse functions of certain classes of univalent functions

Vasudevarao Allu; Vibhuti Arora

paper

Initial Successive coefficients of Inverse functions of certain classes of univalent functions

arXiv:2111.00505

Abstract

We consider functions of the type $f (z) = z + a_{2} z^{2} + a_{3} z^{3} + \dots$ from a family of all analytic and univalent functions in the unit disk. Let $F$ be the inverse function of $f$ , given by $F (z) = w + \sum_{n = 2}^{\infty} A_{n} w^{n}$ defined on some $∣ w ∣ \leq r_{0} (f)$ . In this paper, we find the sharp bounds of $∣ A_{n + 1} ∣ - ∣ A_{n} ∣$ , for $n = 1, 2$ , for some subclasses of univalent functions.