39 research outputs found
On logarithmic coefficients of some close-to-convex functions
The logarithmic coefficients of an analytic and univalent function
in the unit disk with the
normalization is defined by . Recently, D.K. Thomas [On the logarithmic
coefficients of close to convex functions, {\it Proc. Amer. Math. Soc.} {\bf
144} (2016), 1681--1687] proved that for functions
in a subclass of close-to-convex functions (with argument ) and claimed that
the estimate is sharp by providing a form of a extremal function. In the
present paper, we pointed out that such extremal functions do not exist and the
estimate is not sharp by providing a much more improved bound for the whole
class of close-to-convex functions (with argument ). We also determine a
sharp upper bound of for close-to-convex functions (with argument
) with respect to the Koebe function.Comment: 13 page