Coefficient estimates for inverses of starlike functions of positive order

In the present paper, the coefficient estimates are found for the class S*(-1) (a) consisting of inverses of functions in the class of univalent starlike functions of order a in D = {z is an element of C: vertical bar z vertical bar < 1}. These estimates extend the work of Krzyz, Libera and Zlotkiewicz [J.G. Krzyz, R.J. Libera, E. Zlotkiewicz, Coefficients of inverse of regular starlike functions, Ann. Univ. Mariae Curie- S kl odowska Sect. A 33 (10) (1979) 103-109] who found sharp estimates on only first two coefficients for the functions in the class S*(-1)(a). The coefficient estimates are also found for the class Sigma*(-1) (alpha), consisting of inverses of functions in the class Z*(ce) of univalent starlike functions of order alpha in V = {z is an element of C: 1 < vertical bar z vertical bar < infinity}. The open problem of finding sharp coefficient estimates for functions in the class Z*(a) stands completely settled in the present work by our method developed here. (c) 2006 Elsevier Inc. All rights reserved.