TY - JOUR
T1 - Symmetrization of Suffridge polynomials and approximation of T-symmetric Koebe functions
AU - Dmitrishin, Dmitriy
AU - Smorodin, Andrey
AU - Stokolos, Alex
AU - Tohaneanu, Mihai
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/11/15
Y1 - 2021/11/15
N2 - The article studies extremal properties of certain T-symmetric polynomials, which generalize the famous Suffridge polynomials. Our first result establishes an asymptotic estimate for the maximum modulus in the unit disk. Our second result uses these polynomials to approximate univalent functions in the unit disk, which is the analogue of the Andrievskii-Ruscheweych subordination [1] to T-symmetric polynomials. The main technical tool is a limit formula for representing an exponential function as a product of trigonometric functions.
AB - The article studies extremal properties of certain T-symmetric polynomials, which generalize the famous Suffridge polynomials. Our first result establishes an asymptotic estimate for the maximum modulus in the unit disk. Our second result uses these polynomials to approximate univalent functions in the unit disk, which is the analogue of the Andrievskii-Ruscheweych subordination [1] to T-symmetric polynomials. The main technical tool is a limit formula for representing an exponential function as a product of trigonometric functions.
KW - Suffridge polynomials
KW - T-symmetric Koebe function
KW - T-symmetric univalent polynomials
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U2 - 10.1016/j.jmaa.2021.125350
DO - 10.1016/j.jmaa.2021.125350
M3 - Article
AN - SCOPUS:85106350019
SN - 0022-247X
VL - 503
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 125350
ER -