Logarithmic coefficient bounds for the class of Bazilevic functions

If S denotes the class of all univalent functions in the open unit disk D := {z is an element of C : vertical bar z vertical bar < 1} with the form f (z) = z + Sigma(infinity)(n=2) a(n)z(n), then 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(f)z(n), z is an element of D. The logarithmic coefficients were brought to the forefront by I.M. Milin in the 1960's as a method of calculating the coefficients a(n) for f is an element of S. He concerned himself with logarithmic coefficients and their role in the theory of univalent functions, while in 1965 Bazilevic also pointed out that the logarithmic coefficients are crucial in problems concerning the coefficients of univalent functions. In this paper we estimate the bounds for the logarithmic coefficients vertical bar gamma(n)(f)vertical bar when f belongs to the class B(alpha, beta) of Bazilevic function of type (alpha, beta).