Geodesic
Exact estimates and radii of convexity of some classes of analytic functions
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 14 (2022) no. 1, pp. 42-49

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The study of the geometric properties of analytic functions is one of the classical problems of the theory of functions of a complex variable and has been of steady interest to many mathematicians for more than half a century now. At the same time, a separate area is the building of sufficient conditions of one-leaf analytic functions, including finding the conditions for simple geometric properties of analytic functions (convex or star-shaped, almost starshaped, etc.). The solution of these problems in many cases is associated with finding estimates in different classes of analytical functions, which in itself is also a relevant problem. This article is devoted to finding exact estimates of analytic functions and their derivatives in fairly broad classes of functions, which are distinguished in the form of some restrictions on the domains obtained from the domains of values of these functions by circular symmetrization or symmetrization with respect to a straight line. Based on these results, the exact radii of convexity in some classes of functions are found.
Keywords: geometric theory of functions of a complex variable, domain symmetrization, estimates of analytic functions, one-leaf functions, radii of convexity of analytic functions. 
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     author = {F. F. Maiyer and M. G. Tastanov and A. A. Utemissova and S. A. Kozlovskiy},
     title = {Exact estimates and radii of convexity of some classes of analytic functions},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
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     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2022_14_1_a4/}
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F. F. Maiyer; M. G. Tastanov; A. A. Utemissova; S. A. Kozlovskiy. Exact estimates and radii of convexity of some classes of analytic functions. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 14 (2022) no. 1, pp. 42-49. http://geodesic.mathdoc.fr/item/VYURM_2022_14_1_a4/