Logarithmic coefficients of some close-to-convex functions

Abstract

The logarithmic coefficients ${\gamma }_n$ of an analytic and univalent function $f$ in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f^{\prime }(0)-1$ are defined by $\log \frac{f(z)}{z}=2{\sum }_{n=1}^{\infty }{\gamma }_n{z}^n$. In the present paper, we consider close-to-convex functions (with argument $0$) with respect to odd starlike functions and determine the sharp upper bound of $|{\gamma }_n|$, $n=1,2,3$ for such functions $f$.

09 pages. arXiv admin note: substantial text overlap with arXiv:1606.05162

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• Logarithmic coefficients of close-to-convex functions