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

Abstract

We consider functions of the type f (z) = z + a 2 z 2 + a 3 z 3 + • • • 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 + ∞ n=2 A n w n defined on some |w| ≤ 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.