由Sălăvgean-q微分算子定义的具有对称共轭点的单叶调和函数类
A Class of Univalent Harmonic Functions with Symmetric Conjugate Points Defined by the Sălăgean-q Differential Operator
DOI: 10.12677/pm.2024.147277, PDF,    科研立项经费支持
作者: 马丽娜, 李书海：赤峰学院数学与计算机科学学院，内蒙古 赤峰
关键词: 对称共轭点；Sălăgean；q微分算子；调和函数；Fekete-Szegö不等式；Symmetric Conjugate Points； Sălăgean； q Differential Operator； Harmonic Function； Fekete-Szegö Inequality
摘要: 在单复变函数几何理论的研究中，构造函数类及研究它的几何性质是目前国内外重要的研究课题。本文首先定义了一个Sălăgean-q微分算子，利用该算子，我们构建了一类具有特殊性质的倒结构单叶调和函数，这类函数具有对称共轭点。我们进一步推导出了这类函数的系数条件，并得到了相应的Fekete-Szegö不等式，这一发现有效地拓展了现有的知识范畴。这一成果不仅丰富了单复变函数的理论内容，也为调和函数的研究提供了新的视角和方法。更重要的是，这一研究可能为未来在信号处理、图像处理等领域的实际应用提供新的数学模型和算法基础。
Abstract: In the study of the geometric theory of simple complex functions, constructing the function class and studying its geometric properties are important research topics at home and abroad. In this paper, a Sălăgean-q differential operator is first defined. Using the operator, we constructed a class of univalent harmonic functions with inverse structure and special properties. This class of function has symmetric conjugate points. We further derived the coefficient conditions for functions of the class and obtained the corresponding Fekete-Szegö inequality. This discovery effectively expands the existing knowledge scope. This achievement not only enriches the theoretical content of simple complex functions, but also provides a new perspective and method for the study of harmonic functions. More importantly, this research may provide a new mathematical model and algorithm basis for practical applications in signal processing, image processing and other fields in the future.
文章引用：马丽娜, 李书海. 由Sălăvgean-q微分算子定义的具有对称共轭点的单叶调和函数类[J]. 理论数学, 2024, 14(7): 103-112. https://doi.org/10.12677/pm.2024.147277

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