Integral means of analytic functions

For analytic functions f(z) and g(z) which satisfy the subordination f(z)≺g(z), J.E. Littlewood [Proc. London Math. Soc. 23 (1925) 481-519] has shown some interesting results for integral means of f(z) and g(z). The object of the present paper is to derive some applications of integral means by J.E. Littlewood. We also show interesting examples for our theorems.