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Analytic functions with polar and logarithmic singularities and locally convex boundary values

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Abstract

We consider a family of functions which have a pole of order m and a logarithmic term at the infinity and generalize univalent convex functions defined in the exterior of the unit disc. We prove sharp estimates for the derivative and the Schwarzian and describe some geometric properties of such functions.

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Correspondence to F. G. Avkhadiev.

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The work is supported by RFBR, grants 11-01-00762-a, 12-01-00636-a.

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Avkhadiev, F.G. Analytic functions with polar and logarithmic singularities and locally convex boundary values. Lobachevskii J Math 33, 208–215 (2012). https://doi.org/10.1134/S1995080212030043

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  • DOI: https://doi.org/10.1134/S1995080212030043

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