论文标题
Sakaguchi课程的第五系数和Hermitian-toeplitz的尖锐界限
Sharp Bounds of Fifth Coefficient and Hermitian-Toeplitz determinants for Sakaguchi Classes
论文作者
论文摘要
对于分析函数的类别，在单位磁盘上定义的$ f $满足满足$ \ frac {z {f}'（z）} {f（z）} {f（z） - f（z）} \precφ（z）\ quad \ quad \ quad \ text {and} \ quard {and} \ quad \ quad \ quad \ frac \ frac \ frac {（2 z {Z {Z {Z）'（Z）'（Z）'（Z）'（Z）'（Z）'}'''''''''''''''''（''（Z）'}'}''''（''（F） \precφ（z），$$由$ \ MATHCAL {s}^*_ s（φ）$和$ \ MATHCAL {C} _S（φ）$分别表示，$ n^{th} $ taylor系数的尖锐界限是$ n = 2，$ n = 2，$ 3 $ 3 $和$ 3 $和$ 3 $和$ 3 $和$ 3 $。在本文中，我们获得了第五系数的锐角。此外，确定了属于这些类别的功能的三阶Hermitian toeplitz决定因素的尖锐和上部估计值。我们的结果的应用导致建立某些新的和先前已知的结果。
For the classes of analytic functions $f$ defined on the unit disk satisfying $$\frac{z {f}'(z)}{f(z) - f(-z)} \prec φ(z) \quad \text{and} \quad \frac{(2 z {f}'(z))'}{(f(z) - f(-z))'} \prec φ(z),$$ denoted by $\mathcal{S}^*_s(φ)$ and $\mathcal{C}_s(φ)$ respectively, the sharp bound of the $n^{th}$ Taylor coefficients are known for $n=2,$ $3$ and $4$. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.
