The focus of this article is to explore the Bohr inequality for a specific subset of harmonic starlike mappings introduced by Ghosh and Vasudevarao (Some basic properties of certain subclass of harmonic univalent functions, Complex Var. Elliptic Equ. 63 (2018), no. 12, 1687–1703.). This set is denoted as ℬ H 0 ( M ) ≔ { f = h + g ¯ ∈ ℋ 0 : ∣ z h ″ ( z ) ∣ ≤ M − ∣ z g ″ ( z ) ∣ } {{\mathcal{ {\mathcal B} }}}_{H}^{0}\left(M):= \{f=h+\overline{g}\in {{\mathcal{ {\mathcal H} }}}_{0}:| z{h}^{^{\prime\prime} }\left(z)| \le M-| z{g}^{^{\prime\prime} }\left(z)| \} for z ∈ D z\in {\mathbb{D}} , where 0 < M ≤ 1 0\lt M\le 1 . It is worth mentioning that the functions belonging to the class ℬ H 0 ( M ) {{\mathcal{ {\mathcal B} }}}_{H}^{0}\left(M) are recognized for their stability as starlike harmonic mappings. With this in mind, this research has a twofold goal: first, to determine the optimal Bohr radius for this specific subclass of harmonic mappings, and second, to extend the Bohr-Rogosinski phenomenon to the same subclass.

中文翻译：

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关于稳定星状调和映射特殊子类的玻尔不等式

本文的重点是探索 Ghosh 和 Vasudevarao 引入的调和星状映射的特定子集的玻尔不等式（调和单价函数某些子类的一些基本性质，复杂变量。椭圆方程 63（2018），没有。12, 1687–1703)。该集合表示为 ℬ H 0 （ 中号 ） ≔ { F = H + G ￣ ε ℋ 0 ： ∣ z H ” （ z ） ∣ ≤ 中号 - ∣ z G ” （ z ） ∣ } {{\mathcal{ {\mathcal B} }}}_{H}^{0}\left(M):= \{f=h+\overline{g}\in {{\mathcal{ {\mathcal H} }}}_{0}:| z{h}^{^{\prime\prime} }\left(z)| \le M-| z{g}^{^{\prime\prime} }\left(z)| \} 为了 z ε D z\in {\mathbb{D}} ， 在哪里 0 < 中号 ≤ 1 0\lt M\le 1 。值得一提的是，属于该类的函数 ℬ H 0 （ 中号 ） {{\mathcal{ {\mathcal B} }}}_{H}^{0}\left(M) 因其稳定性而被认为是星状调和映射。考虑到这一点，这项研究有双重目标：首先，确定调和映射的这个特定子类的最佳玻尔半径，其次，将玻尔-罗戈辛斯基现象扩展到同一子类。