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

The logarithmic coefficients gamma(n) of a normalized analytic functions f are defined by (log f (z)/ z) = 2 Sigma(infinity)(n=1)c(n)z(n). For certain closeto-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 gamma(3) when the second coefficient alpha(2) is real. In the present paper, the upper bound of the third logarithmic coefficient gamma(3) is computed with no restriction on the second coefficient alpha(2).