Initial successive coefficients for certain classes of univalent functions

Abstract

We consider a family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2{z}^2+a_3{z}^3+\cdots$. The aim of this article is to investigate the bounds of the difference of moduli of initial successive coefficients, i.e. $||a_{n+1}|-|a_n||$ for $n=1,2$ and for some subclasses of analytic univalent functions. We found that all the estimations are sharp in nature by constructing some extremal functions.