The Third Logarithmic Coefficient For The Subclasses Of Close-To-Convex Functions

Abstract

Let $\mathcal{A}$ denote the set of all analytic functions $f$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ normalized by $f(0)=0$ and $f^{\prime }(0)=1.$ The logarithmic coefficients ${\gamma }_n$ of $f\in \mathcal{A}$ are defined by $\log f(z)/z=2{\sum }_{n=1}^{\infty }{\gamma }_n{z}^n.$ In the present paper, the upper bound of the third logarithmic coefficient in general case of $f^{\prime \prime }(0)$ was computed when $f$ belongs to some familiar subclasses of close-to-convex functions.

6 pages