On the generalization of some classes of close-to-convex and typically real functions | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2023. № 85. DOI: 10.17223/19988621/85/1

On the generalization of some classes of close-to-convex and typically real functions

The paper introduces the class C(λ, α, γ) = { f(z): | ((1 -λz 2)f '(z))1/γ - α |⩽ α }, 0 λ 1, 0 < γ 1, a > 1/2, almost convex order for functions, generalizing classes of functions with limited rotation (α →+∞ λ = 0) and functions convex of order y in the direction of the imaginary axis (α → +∞, λ = 1). For the class C(λ, α, γ) and its subclasses, unimprovable distortion theorems and exact convexity radii are found, and similar results are obtained in a class generalizing the class of typically real functions.

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Keywords

geometric theory of functions, single-leaf functions, estimates of analytic functions, typically real functions, radii of convexity

Authors

Name	Organization	E-mail
Maiyer Fedor F.	Kostanay Regional University named after A. Baitursynov	maiyer@mail.ru
Tastanov Meyrambek G.	Kostanay Regional University named after A. Baitursynov	tastao@mail.ru
Utemissova Anar A.	Kostanay Regional University named after A. Baitursynov	anar_utemisova@mail.ru
Baimankulov Abdykarim T.	Kostanay Regional University named after A. Baitursynov	bat_56@mail.ru

Всего: 4

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