卷积结构与几何函数理论——用以研究特定几何函数理论方向的分数阶微积分算子与卷积结构

本书所介绍的是几何函数理论的一部分，在这个工作中作者研究解析函数的几何行为。黎曼-刘维尔分数算子已经被广泛应用，用以获得许多单叶或多叶解析或亚纯函数的不同子类的性质，例如内含关系、系数估计、偏差定理等。不同的分数算子和卷积结构已经被应用到研究解析和亚纯函数的不同子类的工作中。从属方法、卷积结构和Miller和Mocanu所得到的结果已经被广泛使用，并且在当今研究中得到了许多新的结果。

1 Introduction and preliminary concepts
1.1 Introduction
1.2 Preliminary results and definitions
1.2 1 Starlike functions
1.2 2 Convex functions
1.2 3 Close-to-convex functions
1.2.4 Multivalent functions
1.2.5 Certain classes of meromohic functions
1.2.6 Hadamard product\Convolution
1.2.7 Class P of flmctionswithpositive real part
1.2.8 Differential subordination and superordination
1.2.9 Strong differential subordination and superordination
1.2.10 Fractional operators
1.3 Summary
1.4 Glossary
1.5 List of publications
2 Certain New Classes of Analytic Functions
2.1 Introduction and preliminaries
2.2 Main inclusion relationship
2.3 Coefficmestimate
3 Certain Subclasses of p-Valent Analytic Functions
3.1 Introduction and preliminaries
3.2 Main inclusion relationships
3.3 Integral operator
4 A subclass of Close-to-convex Functions with Fekete-Szego Problem
4.1 Introduction and preliminaries
4.2 Properties of starlike functions
4.3 Inclusion relationships
4.4 Coefficm estimates
4.5 Covering theorem
46 Distortion theorem
4.7 Fekete-Szego problem
5 Certain Subclasses of Meromorphic Close-to-convex Functions
5.1 Introduction
5.2 The classes MK(A,B)and MK(t,A,B)
5.2.1 Properties of meromorphic starlike fuuctions
5.2.2 Coefficient estimates
5.2.3 Distortion theorem
5.3 The class MK(k)(λ,μ,A,B)
5.3.1 Properties ofthe class MS*(α,β)
6 Differential Subordination and Superordination results for pvalent Analytic Functions
6.1 Introduction and preliminaries
6.2 Main results
6.3 Superordination results
7 Strong Differential Subordination and Superordination
7.1 Introduction and definitions
7.2 Main results
7.3 Superordination resultsforthe operatorIδc,p
编辑手记