论文标题
Bohr现象，用于某些近接头分析功能
Bohr phenomenon for certain close-to-convex analytic functions
论文作者
论文摘要
我们说分析函数的类$ \ Mathcal {b} $ $ f（z）= \ sum_ {n = 0}^{\ infty} a_ {n} z^{n} z^{n} $在单位disk $ \ mathb {d}中bohr现象，如果最大的半径$ r_ {f} <1 $，以下不等式$ \ sum \ limits_ {n = 1}^{\ infty} | a__ {n} z^Z^{n} | \ leq d（f（f（0），\ partial f（\ mathbb {d}））$$适用于$ | z | = r \ leq r_ {f} $，以及所有函数$ f \ in \ inthcal {b} $。最大的半径$ r_ {f} $称为$ \ mathcal {b} $的bohr半径。在本文中，我们获得了近距离分析功能的某些子类的BOHR半径。我们为某些分析类建立了bohr现象，$ \ MATHCAL {s} _ {c}^{*}（ϕ），\，\，\，\ Mathcal {c} _ {c} _ {c}（ϕ），\，\，\，\，\，\ Mathcal {c} _ {c} _ {s} _ {s}^{*}^{*}}}}}（every） \ Mathcal {k} _ {s}（ϕ）$。使用Bohr现象用于从属类\ cite [Lemma 1] {Bhowmik-2018}，我们获得了一些半径$ r_ {f} $，因此这些类的bohr现象适用于$ | z | = r \ leq r_ {f} $。通常，在这种情况下，$ r_ {f} $不必尖锐，但是我们表明，在$ ϕ $上的某些其他条件下，半径$ r_ {f} $变为锐利。由于这些结果，我们在上述类别上获得了几种关于Bohr现象的有趣推论。
We say that a class $\mathcal{B}$ of analytic functions $f$ of the form $f(z)=\sum_{n=0}^{\infty} a_{n}z^{n}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}: |z|<1\}$ satisfies a Bohr phenomenon if for the largest radius $R_{f}<1$, the following inequality $$ \sum\limits_{n=1}^{\infty} |a_{n}z^{n}| \leq d(f(0),\partial f(\mathbb{D}) ) $$ holds for $|z|=r\leq R_{f}$ and for all functions $f \in \mathcal{B}$. The largest radius $R_{f}$ is called Bohr radius for the class $\mathcal{B}$. In this article, we obtain Bohr radius for certain subclasses of close-to-convex analytic functions. We establish the Bohr phenomenon for certain analytic classes $\mathcal{S}_{c}^{*}(ϕ),\,\mathcal{C}_{c}(ϕ),\, \mathcal{C}_{s}^{*}(ϕ),\, \mathcal{K}_{s}(ϕ)$. Using Bohr phenomenon for subordination classes \cite[Lemma 1]{bhowmik-2018}, we obtain some radius $R_{f}$ such that Bohr phenomenon for these classes holds for $|z|=r\leq R_{f}$. Generally, in this case $R_{f}$ need not be sharp, but we show that under some additional conditions on $ϕ$, the radius $R_{f}$ becomes sharp bound. As a consequence of these results, we obtain several interesting corollaries on Bohr phenomenon for the aforesaid classes.
