Publications
Article · Vestnik Tomskogo gosudarstvennogo universiteta Matematika i mekhanika · January 1, 2023
On the generalization of some classes of close-to-convex and typically real functions
Fedor F. Maiyer, Мейрамбек Габдулиевич Тастанов, Anar A. Utemissova, A. Т. Baimankulov
Abstract
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.
Analytic and geometric function theoryHolomorphic and Operator TheoryApproximation Theory and Sequence Spacesclose-to-convex functionstypically real functionsanalytic function classes
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