Univalence of $T$-symmetric Suffridge type polynomials of degree $3T+1$

Abstract

We show the univalence of $T$-symmetric Suffridge type polynomials $S_4^{(T)}$ in the unit disk, confirming thereby the conjecture proposed by Dmitrishin, Gray, and Stokolos in their recent paper. The result also implies the quasi-extremality of $S_n^{(T)}$ in the sense of Ruscheweyh.

8 pages