Abstract
In this article, we prove inequalities for the Taylor coefficients of functions G holomorphic in the unit disc satisfying the condition \(|G(z)|(1-|z|^2)^{\alpha }\le 1, |z|<1,\) for fixed \(\alpha \ge 0.\) The upper bound for the modulus of the k-th Taylor coefficient is dependent on the moduli of some initial coefficients. As corollaries we get similar estimates for \(\alpha \)-Bloch functions and an estimate for an area type functional on \(\alpha \)-Bloch functions.
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Acknowledgements
The authors thank H. Schellwat from Örebro University for his help. He made reference [3] available for them. The research of I. Kayumov was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project No. 1.13556.2019/13.1
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Kayumov, I.R., Wirths, KJ. Inequalities of Carlson Type for \(\alpha \)-Bloch Functions. Mediterr. J. Math. 17, 83 (2020). https://doi.org/10.1007/s00009-020-01519-1
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DOI: https://doi.org/10.1007/s00009-020-01519-1