The second Hankel determinant of logarithmic coefficients and logarithmic inverse coefficients for the class of bounded turning functions of order α

In this paper, we obtain sharp bounds for the second Hankel determinant of logarithmic coefficients H2,1(Ff/2) of bounded turning functions of order alpha. Furthermore, we obtain sharp bounds of the second Hankel determinant of logarithmic inverse coefficients of H-2,H-1(Ff-1/2), where f(-1) is the inverse function of f. For the class P '(alpha), we conclude that the bounds for H2,1(F-f /2) and H-2,H-1(Ff-1/2) are the same only for 1/4 <= alpha < 1.