And A Class Of Integral Operators Associated With Sandwich-type Theorem

Complex analysis is the mathematics theory of studying on the complex functions, especially on meromorphic functions and analytic functions.It is one branch of mathematics with ancient and rich life, which is a classical research field and has attracted great attention of many mathematicians. In recent years, more and more academics working on the sandwich-type theorem about analytic functions, such as Aouf, Miller, Cho, and so on. They obtained some sandwich-type theorems by studying subordination and superordination preserving properties for some operators defined on analytic function. Aouf haved obtained the relation with and D means certain linear operators.Inspired by the ideas of the above articles, the article defines a new class of integral operator denoted by I. In this paper, we obtain some subordination and superordination preserving properties of analytic function involving the integral operators. sandwich-type theorems are also obtained.The whole paper consists of three parts. Each of the components is given as follows:The first part is introduction:we introduce some basic and classical concepts for the investigation of the work presented in this thesis.Such as:Differential subordination, Differential superordination, Subordination Chain, Aρ and Iintegral operator.The second part lists some relative lemmas:which makes preparation for the third part.The third part gives the main results:We study and use the methods of differential subordination and differential superordination to obtain sandwich-type results about I integral operator and inferences.