单叶解析函数强微分超属的最佳从属

Best Subordination of Strong Differential Hypergenus of Univalent Analytic Functions

复分析是研究复函数,特别是解析函数的数学理论,是古老而富有生命的数学分支之一,是一个经典的研究领域。近年来,越来越多的学者研究微分从属和强微分超属,其理论与方法不反应用于泛函分析、拓扑学、微分几何等数学分支,还涉及自然科学的诸多领域,如动力系统、量子力学、信号分析等。因此,对于微分从属和强微分超属的研究具有重要的理论意义与潜在的应用价值。学者OROS G I和OROS G首先引入并研究了强微分超属的概念及其性质,在此基础上,本文引入强微分超属和最佳从属子概念,研究并证明了在单叶解析函数单位圆盘边界未知的情况下,强微分超属的最佳从属子。

Complex analysis is the mathematical theory of studying complex functions,especially analytic functions.It is one of the oldest and most vital branches of mathematics and a classic field of study.Recent years,more and more scholars have studied differential subordination and strong differential hypergenus.Their theories and methods are not only applied to functional analysis,topology,differential geometry and so on,but also to many fields of natural science,such as dynamical system,quantum mechanics,signal analysis and so on.Therefore,the study of differential subordination and strongly differential hypergenus has important theoretical significance and potential application value.Scholars OROS G I and OROS G first introduced and studied the concept of strong differential hypergenus and its properties.On this basis,this paper introduces the concepts of strong differential hypergenus and the best subordinate subgenus,and investigates and proves the best subordinate of strong differential hypergenus for univalent analytic functions with unknown boundary on the unit disk.