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.  2004 Elsevier Inc. All rights reserved