TY - JOUR AU - Chyzhykov, I.E. AU - Mokhon'ko, A.Z. PY - 2020/12/25 Y2 - 2024/03/29 TI - Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane: Logarithmic derivative estimates of meromorphic functions in the half-plane JF - Matematychni Studii JA - Mat. Stud. VL - 54 IS - 2 SE - Articles DO - 10.30970/ms.54.2.172-187 UR - http://matstud.org.ua/ojs/index.php/matstud/article/view/151 SP - 172-187 AB - We established new sharp estimates outside exceptional sets for of the logarithmic derivatives $\frac{d^ {k} \log f(z)}{dz^k}$ and its generalization $\frac{f^{(k)}(z)}{f^{(j)}(z)}$, where $f$ is a meromorphic function $f$ in the upper half-plane, $k>j\ge0$ are integers. These estimates improve known estimates due to the second author in the class of meromorphic functions of finite order.Examples show that size of exceptional sets are best possible in some sense. ER -