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The logarithmic coefficients of an analytic and univalent function in the unit disk with the normalization are defined by . Recently, DK Thomas [Proc. Amer. Math. Soc. 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 an extremal function. In the present paper, we point 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. References