In this paper, we study the Bohr phenomenon for functions that are defined on a general simply connected domain of the complex plane. We improve known results of R. Fournier and St. Ruscheweyh for a class of analytic functions. Furthermore, we examine the case where a harmonic mapping is defined in a disk containing $${\mathbb {D}}$$ D and obtain a Bohr type inequality.

中文翻译：

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改进了移动磁盘的玻尔不等式

在本文中，我们研究了在复平面的一般单连通域上定义的函数的玻尔现象。我们改进了 R. Fournier 和 St. Ruscheweyh 对一类解析函数的已知结果。此外，我们检查在包含 $${\mathbb {D}}$$ D 的磁盘中定义调和映射的情况，并获得 Bohr 类型不等式。