Pre-Schwarzian and Schwarzian norm estimates for subclasses of univalent functions

Xiaoyuan Wang, Huijie Li, Jinhua Fan
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Abstract

In the present article, we are focused to study the sharp estimates of the pre-Schwarzian and Schwarzian norms for subclasses of univalent functions. We will generalize the results of Carrasco and Hernández (Anal Math Phys 13(2):22, 2023) to the case of Janowski convex mappings in terms of the value \(h^{\prime \prime }(0)\). We will also derive the sharp bound of pre-Schwarzian norm for a subclass of harmonic mappings whose fixed analytic part is a convex function of order \(\alpha (0 \le \alpha <1)\).

单值函数子类的前施瓦兹和施瓦兹规范估计值
在本文中,我们将重点研究单值函数子类的前施瓦兹规范和施瓦兹规范的尖锐估计。我们将把 Carrasco 和 Hernández (Anal Math Phys 13(2):22, 2023) 的结果推广到 Janowski 凸映射的情况,即值 \(h^\{prime \prime }(0)\)。我们还将推导出固定解析部分是阶为 \(α (0 \le \alpha <1)\)的凸函数的调和映射子类的前施瓦茨规范的尖界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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