Schwarz's lemma and estimates of coefficients for regular functions with free domain of definition

V. N. Dubinin

Sbornik. Mathematics, Tome 196 (2005) no. 11, pp. 1605-1625

Résumé

On the basis of a sufficient condition for univalency and classical properties of conformal maps new versions of Schwarz's inequalities for regular functions with free domain of definition are obtained, refined, and supplemented. Estimates for coefficients of the expansions of such functions are obtained and applied to inequalities for algebraic polynomials.

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