Logarithmic coefficients for certain subclasses of close-to-convex functions

Let S denote the class of functions analytic and univalent (i.e. one-to-one) in the unit disk D = {z is an element of C : vertical bar z vertical bar < 1} normalized by f (0) = 0 = f'(0) - 1. The logarithmic coefficients gamma(n) of f is an element of S are defined by log f (z)/z = 2 Sigma(infinity)(n=1) gamma(n)z(n). Let F-1(F-2 and F-3 resp.) denote the class of functions f is an element of A such that Re (1-z) f'(z) > 0 (Re (1 - z(2)) f' (z) > 0 and Re (1 - z + z(2)) f' (z) > 0 resp.) in D. The classes F-1, F-2 and F-3 are subclasses of the class of close-to-convex functions. In the present paper, we determine the sharp upper bound for vertical bar gamma(1)vertical bar, vertical bar gamma(2)vertical bar and vertical bar gamma(3)vertical bar for functions f in the classes F-1, F-2 and F-3.