On the successive coefficients of close-to-convex functions

Let f ∈ S, f be a close-to-convex function, fk(z) = [f (zk)]1/k. The relative growth of successive coefficients of fk(z) is investigated. The sharp estimate of ||cn+1| − |cn|| is obtained by using the method of the subordination function.  2003 Published by Elsevier Inc