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For a meromorphic function $f$ in the unit disk $U=\{z:\;|z| Click to show full abstract
For a meromorphic function $f$ in the unit disk $U=\{z:\;|z|<1\}$ and arbitrary points $z_1,z_2$ in $U$ distinct from the poles of $f$, a sharp upper bound on the product $|f'(z_1)f'(z_2)|$ is established. Further, we prove a sharp distortion theorem involving the derivatives $f'(z_1)$, $f'(z_2)$ and the Schwarzian derivatives $S_f(z_1)$, $S_f(z_2)$ for $z_1,z_2\in U$. Both estimates hold true under some geometric restrictions on the image $f(U)$.
Keywords:
distortion theorems;
schwarzian derivatives;
distortion;
theorems schwarzian;
two point;
point distortion
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!