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

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