The Third Logarithmic Coefficient for Certain Close-to-Convex Functions

Abstract

The logarithmic coefficients γn of a normalized analytic functions f are defined by log fz/z=2∑n=1∞γnzn. For certain close-to-convex functions fz=z+a2z2+⋯, Cho et al. (on the third logarithmic coefficient in some subclasses of close-to-convex functions) has obtained the upper bound of the third logarithmic coefficient γ3 when the second coefficient a2 is real. In the present paper, the upper bound of the third logarithmic coefficient γ3 is computed with no restriction on the second coefficient a2.