论文标题
某些非无价分析功能的理论
Theory of certain Non-Univalent Analytic functions
论文作者
论文摘要
我们研究了非无界函数的特性，让人想起单相类似函数的理论。令分析函数$ψ（z）= \ sum_ {i = 1}^{\ infty} a_i z^i $，$ a_1 \ neq0 $在单位磁盘中是无用的。可以在类别$ f（z）= z+\ sum_ {k = 2}^{\ iftty} a_k z^k^k $满意$（Zf'（zf'（zf'（zf'（zf'（zf''（zf（z）}/} $）），$ f（z）= z+f（z）= 2}^a分析函数$ \ mathcal {f}（ψ）$可以在类$ \ mathcal {f}（ψ）$中找到非义函数。这样的功能，例如MA和Minda类别类似Star的功能，也具有不错的几何特性。对于这些功能，已经建立了生长和失真定理。此外，我们获得了一些尖锐系数功能的界限，并为$ \ Mathcal {f}（ψ）$的类Bohr和Rogosinki现象建立了界限。共享分析函数特性的非分析函数称为多分析函数。此外，我们计算Bohr和Rogosinski的半径，用于与分析功能的多分析功能，在类$ \ Mathcal {f}（ψ）$或Ma-Minda Starlike和convex函数的类中。
We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function $ψ(z)=\sum_{i=1}^{\infty}A_i z^i$, $A_1\neq0$ be univalent in the unit disk. Non-univalent functions may be found in the class $\mathcal{F}(ψ)$ of analytic functions $f$ of the form $f(z)=z+\sum_{k=2}^{\infty}a_k z^k$ satisfying $({zf'(z)}/{f(z)}-1) \prec ψ(z)$. Such functions, like the Ma and Minda classes of starlike functions, also have nice geometric properties. For these functions, growth and distortion theorems have been established. Further, we obtain bounds for some sharp coefficient functionals and establish the Bohr and Rogosinki phenomenon for the class $\mathcal{F}(ψ)$. Non-analytic functions that share properties of analytic functions are known as Poly-analytic functions. Moreover, we compute Bohr and Rogosinski's radius for Poly-analytic functions with analytic counterparts in the class $\mathcal{F}(ψ)$ or classes of Ma-Minda starlike and convex functions.
