LOGARITHMIC COEFFICIENTS OF SOME CLOSE-TO-CONVEX FUNCTIONS

Abstract

The logarithmic coefficients$\unicode[STIX]{x1D6FE}_{n}$of an analytic and univalent function$f$in the unit disc$\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$with the normalisation$f(0)=0=f^{\prime }(0)-1$are defined by$\log (f(z)/z)=2\sum _{n=1}^{\infty }\unicode[STIX]{x1D6FE}_{n}z^{n}$. 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$|\unicode[STIX]{x1D6FE}_{n}|$,$n=1,2,3$, for such functions $f$.