Abstract
Let \(\mathcal{B}\) denote the class of all analytic functions \(f(z)=\sum_{k=0}^{\infty}a_{k}z^{k}\) mapping the unit disk into itself. We consider the powered Bohr sum \(M_{p}^{f}(r)=\sum_{k=0}^{\infty}|a_{k}|^{p}r^{k}\) with an additional term including the area of the Riemann surface which is the image of the disk \(\{|z|<r\}\). In this setting, we prove the counterpart of the Bohr theorem for two cases, considering different values of the zero coefficient \(a_{0}=f(0)\).
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The work of the author was carried out within the framework of the development program of the Scientific and Educational Mathematical Center of the Volga Federal District, agreement no. 075-02-2022-882.
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Khammatova, D.M. Refinement of Powered Bohr Inequality. Lobachevskii J Math 43, 2954–2960 (2022). https://doi.org/10.1134/S1995080222130194
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DOI: https://doi.org/10.1134/S1995080222130194