ON A SPECIAL CLASS OF SCHWARTZ FUNCTIONS
ON A SPECIAL CLASS OF SCHWARTZ FUNCTIONS
In this paper we study functions $ \omega(z) = c_1z+c_2z^2+c_3z^3+\cdots$ analytic in the open unit disk $\D$ and such that $|\omega'(z)|\le1$ for all $z\in\D$. For these functions we give estimates (sometimes sharp) for the following moduli: $|c_3-c_1c_2|$, $|c_1c_3-c_2^2|$, and $|c_4-c_2^2|$.