On logarithmic coefficients for classes of analytic functions associated with convex functions

Abstract

Let S denote the class of analytic and univalent functions in the unit disk D={z∈C:|z|<1} of the form f(z)=z+∑n=2∞anzn. For f∈S, the logarithmic coefficients defined by log⁡(f(z)/z)=2∑n=1∞γnzn,z∈D. In 1971, Milin [12] proposed a system of inequalities for the logarithmic coefficients of S. This is known as the Milin conjecture and implies the Robertson conjecture which implies the Bieberbach conjecture for the class S. Recently, the other interesting inequalities involving logarithmic coefficients for functions in S and some of its subfamilies have been studied by Roth [24], and Ponnusamy et al. [17]. In this article, we estimate the logarithmic coefficient inequalities for certain subfamilies of Ma-Minda family defined by a subordination relation. It is important to note that the inequalities presented in this study would generalize some of the earlier work.