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

Abstract

The logarithmic coefficients γ n of a normalized analytic functions f are defined by log f z / z = 2 ∑ n = 1 ∞ γ n z n . For certain close-to-convex functions f z = z + a 2 z 2 + ⋯ , 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 γ 3 when the second coefficient a 2 is real. In the present paper, the upper bound of the third logarithmic coefficient γ 3 is computed with no restriction on the second coefficient a 2 .