Univalence criteria for locally univalent analytic functions

Zhenyong Hu; Jinhua Fan; Xiaoyuan Wang

doi:10.37863/umzh.v75i7.7222

Zhenyong Hu School of Mathematics and Statistics, Nanjing University of Science and Technology, China
Jinhua Fan School of Mathematics and Statistics, Nanjing University of Science and Technology, China
Xiaoyuan Wang School of Mathematics and Statistics, Nanjing University of Science and Technology, China

DOI: https://doi.org/10.37863/umzh.v75i7.7222

Анотація

УДК 517.5

Критерії однозначності для локально однозначних аналітичних функцій

Припустимо, що $p(z)=1+z\phi''(z)/\phi'(z),$ де $\phi(z)$ – локально однозначна аналітична функція в одиничному диску $\mathbf{D}$ з $\phi(0)=\phi'(1)-1=0.$ Отримано нижню та верхню оцінки для найкращих сталих $\sigma_{0}$ та $\sigma_{1},$ таких що $e^{-\sigma_{0}/2}<|p(z)|<e^{\sigma_{0}/2}$ і $|p(w)/p(z)|<e^{\sigma_{1}}$ для $z, w\in\mathbf{D}$ відповідно означають однозначність $\phi(z)$ в $\mathbf{D}. $

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