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arXiv 2602.136132026-02-14math.CV

关于Clunie和Sheil-Small关于单值调和映射系数猜想的注记

Note on the Coefficient Conjecture of Clunie and Sheil-Small on the univalent harmonic mapping

Shri Ramswaroop Memorial University（斯里·兰斯瓦罗普纪念大学）；Istanbul Kültür University（伊斯坦布尔文化大学）

Omendra Mishra, Asena Çetinkaya

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AI总结：

本文通过构造广义单值调和映射并提出反例，验证并改进了Clunie和Sheil-Small关于单值调和映射系数猜想的界。

摘要：

在本文中，我们构造了广义的单值调和映射，并找到了其系数界。我们通过这些例子提出反例，以验证Clunie和Sheil-Small为函数$f = h + \overline{g} \in \mathcal{S}_{\mathcal{H}}$提出的系数猜想，并利用这些例子改进了$\mathcal{S}_{\mathcal{H}}$类的猜想界。

英文摘要：

In this article, we construct generalized harmonic univalent mappings and find its coefficients bounds. We present the counterexample to validate the coefficient conjecture proposed by Clunie and Sheil-Small for the class of functions $f=h+\overline{g}\in \mathcal{S}_{\mathcal{H}}$ with the help of these examples we improve the conjecture bounds of class $\mathcal{S}_{\mathcal{H}}$.

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