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SOURCE:    Almanac of Modern Science and Education. Tambov: Gramota, 2015. № 9. P. 122-125.
SCIENTIFIC AREA:    Physical-Mathematical Sciences
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TAYLOR COEFFICIENTS DEPENDENCE ON REINHARDT DOMAINS BOUNDARIES PARAMETERIZATION RADIUSES
Sultygov Magomet Dzhabrailovich
Ingush State University
Abstract. The dependence of Taylor coefficients on Reinhardt domains boundaries parameterization radiuses for various classes of holomorphic functions is shown. For star-convex functions the estimations of Taylor coefficients in bicircle are obtained. For Mocanu functions of order ? - in hypersphere, and in hypercone the estimations of Taylor coefficients for star functions of type ? and order ? are obtained. In the last example the estimations of Taylor coefficients of the class of spiral-shaped functions in specific logarithmically convex limited full double-circled domain are presented.
Key words and phrases: коэффициенты Тейлора, радиусы параметризации границы, области Рейнхарта, бикруг, гипершар, гиперконус, звездно-выпуклые функции, тип, порядок, двоякокруговая область, Taylor coefficients, radiuses of boundary parameterization, Reinhardt domains, bicircle, hypersphere, hypercone, star-convex functions, type, order, double-circled domain
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