ON OZAKI CLOSE-TO-CONVEX FUNCTIONS

Abstract

Let $f$ be analytic in $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ and given by $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$ . We give sharp bounds for the initial coefficients of the Taylor expansion of such functions in the class of strongly Ozaki close-to-convex functions, and of the initial coefficients of the inverse function, together with some growth estimates.