Abstract
For meromorphic circumferentially mean p-valent functions, an analog of the classical distortion theorem is proved. It is shown that the existence of connected lemniscates of the function and a constraint on a cover of two given points lead to an inequality involving the Green energy of a discrete signedmeasure concentrated at the zeros of the given function and the absolute values of its derivatives at these zeros. This inequality is an equality for the superposition of a certain univalent function and an appropriate Zolotarev fraction.
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Original Russian Text © V. N. Dubinin, 2018, published in Matematicheskie Zametki, 2018, Vol. 104, No. 5, pp. 700–707.
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Dubinin, V.N. Lemniscate Zone and Distortion Theorems for Multivalent Functions. II. Math Notes 104, 683–688 (2018). https://doi.org/10.1134/S0001434618110081
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DOI: https://doi.org/10.1134/S0001434618110081