Abstract:
In this paper we study the behavior of the coefficients of functions $\varphi(z)=1+\sum_{k=1}^\infty b_kz^k$,
univalent in the disk $|z|<1$ and assuming there are no pair of values $W$ and $-W$.
In particular, we establish the asymptotic behavior of $b_n$ ($n\to\infty$);
for the coefficients we obtain the estimate $|b_n|<2,34\exp\{1/4n\}$ ($n=2,3,\dots$) and
for each function of the class indicated we prove, subject to a certain condition,
the relationship $||b_{n+1}|-|b_n||=O(n^{-1/2})$.
Fulltext:
PDF file (1026 kB)
