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  to T-symmetric polynomials. The main technical tool is a limit formula for representing an exponential function as a product of trigonometric functions.
|Journal||Journal of Mathematical Analysis and Applications|
|State||Published - Nov 15 2021|
Bibliographical noteFunding Information:
M.T. is partially supported by a grant from the Simons Foundation (# 586051 ).
© 2021 Elsevier Inc.
- Suffridge polynomials
- T-symmetric Koebe function
- T-symmetric univalent polynomials
ASJC Scopus subject areas
- Applied Mathematics