Coefficient estimates for inverses of starlike functions of positive order

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In the present paper, the coefficient estimates are found for the class S ∗ − 1 ( α ) consisting of inverses of functions in the class of univalent starlike functions of order α in D = { z ∈ C : | z | < 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-Sklodowska Sect. A 33 (10) (1979) 103–109] who found sharp estimates on only first two coefficients for the functions in the class S ∗ − 1 ( α ) . The coefficient estimates are also found for the class Σ ∗ − 1 ( α ) , consisting of inverses of functions in the class Σ ∗ ( α ) of univalent starlike functions of order α in V = { z ∈ C : 1 < | z | < ∞ } . The open problem of finding sharp coefficient estimates for functions in the class Σ ∗ ( α ) stands completely settled in the present work by our method developed here.