Sharp Estimates of the First Coefficients for a Class of Typically Real Functions

Abstract

Let T be the class of functions \( f(z)=z+{\displaystyle \sum_{n=2}^{\infty }{c}_n{z}^n} \) regular and typically real in the disk U = {|z| < 1}. Sharp estimates on the coefficients c₅ and c₆ in terms of the values f(r), 0 < r < 1, are obtained.