论文标题
改善了某些谐波单价功能的BOHR不平等现象
Improved Bohr inequalities for certain class of harmonic univalent functions
论文作者
论文摘要
令$ \ Mathcal {h} $为复杂值的谐波映射$ f = h+f = h+\ bar {g} $在单位磁盘$ \ mathbb {d}中定义归一化$ h（0）= 0 = h^{\ prime}（0）-1 $和$ g（0）= 0 $。令$ \ Mathcal {h} _ {0} = \ {f = h+\ bar {g} \ in \ Mathcal {h}：g^{\ prime}（0）= 0 \}。 $ ghosh and vasudevrao \ cite {ghosh-vasudevarao-bams-2020}已经研究了以下有趣的谐波单价类$ \ mathcal {p}^{0} _ {\ Mathcal {\ Mathcal {h}}（M） $ \ MATHCAL {p}^{0} _ {\ Mathcal {h}}（m）：= \ {f = h+\+\ overline {g} \ in \ mathcal {h} _ {h} _ {0} _ {0} -m+| zg^{\ prime \ prime}（z）|，\; z \ in \ mathbb {d} \; \ mbox {and} \; \; \; m> 0 \}。 $$在本文中，我们获得了尖锐的bohr-rogosinski不平等，改善的bohr不平等，精致的bohr不平等和bohr-type不平等，用于$ \ mathcal {p} _ {\ mathcal {\ mathcal {h}}}}}}^0} {0}（m）$。
Let $ \mathcal{H} $ be the class of complex-valued harmonic mappings $ f=h+\bar{g}$ defined in the unit disk $ \mathbb{D} : =\{z\in\mathbb{C} : |z|<1\} $, where $ h $ and $ g $ are analytic functions in $ \mathbb{D} $ with the normalization $ h(0)=0=h^{\prime}(0)-1 $ and $ g(0)=0 $. Let $ \mathcal{H}_{0}=\{f=h+\bar{g}\in\mathcal{H} : g^{\prime}(0)=0\}. $ Ghosh and Vasudevrao \cite{Ghosh-Vasudevarao-BAMS-2020} have studied the following interesting harmonic univalent class $ \mathcal{P}^{0}_{\mathcal{H}}(M) $ which is defined by $$\mathcal{P}^{0}_{\mathcal{H}}(M) :=\{f=h+\overline{g} \in \mathcal{H}_{0}: \mathrm{Re} (zh^{\prime\prime}(z))> -M+|zg^{\prime\prime}(z)|,\; z \in \mathbb{D}\; \mbox{and}\;\; M>0\}. $$ In this paper, we obtain the sharp Bohr-Rogosinski inequality, improved Bohr inequality, refined Bohr inequality and Bohr-type inequality for the class $ \mathcal{P}_{\mathcal{H}}^{0}(M) $.
