局部一元解析函数的一元准则

IF 0.5 4区数学 Q3 MATHEMATICS

Ukrainian Mathematical Journal Pub Date : 2023-11-25 DOI:10.1007/s11253-023-02250-2

Zhenyong Hu, Jinhua Fan, Xiaoyuan Wang

引用次数: 0

摘要

设p(z) = 1 + zϕ″(z)/ϕ ' (z)，其中φ (z)是单位圆盘D中的局部一元解析函数，其中φ (0) = φ '(1)−1 = 0。我们建立了最佳常数σ0和σ1的下界和上界，使得\({e}^{{-\sigma }_{0}/2}<\left|p\left(z\right)\right|<{e}^{{\sigma }_{0}/2}\)和|p(w)/p(z)| ＆lt;\({e}^{{\sigma }_{1}}\)对于z, w∈D，分别表示D中φ (z)的唯一性。

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Univalence Criteria for Locally Univalent Analytic Functions

Suppose that p(z) = 1 + zϕ″(z)/ϕ′(z), where ϕ(z) is a locally univalent analytic function in the unit disk D with ϕ(0) = ϕ′(1) − 1 = 0. We establish the lower and upper bounds for the best constants σ₀ and σ₁ such that \({e}^{{-\sigma }_{0}/2}<\left|p\left(z\right)\right|<{e}^{{\sigma }_{0}/2}\) and |p(w)/p(z)| < \({e}^{{\sigma }_{1}}\) for z, w ∈ D, respectively, imply the univalence of ϕ(z) in D.

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来源期刊

Ukrainian Mathematical Journal MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

107

审稿时长

4-8 weeks

期刊介绍： Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries. Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.