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Abstract In this thesis, by making use of the principle of subordination between analytic functions, we will study various properties of subordination, superordination, sandwich theorems, subordinating factor sequences and inclusion relationships for some new classes associated with different operators. Chapter 1, we give some basic definitions, a brief survey of different linear operators (differential and integral) which will be used in the subsequent chapters. Chapter 2 consists of three sections. Section 2.1 contains the definition of the class , which defined by using the generalized Srivastava Attiya operator Section 2.2, some preliminary lemmas which we will use in this chapter. Section 2.3, different applications of differential subordinations are obtained. Remark 1.The results of this chapter have been published in J. Inequal. Appl. ( see [10]). Chapter 3 consists of four sections. Section 3.1, is an introductory section contains some preliminary lemmas which we will use in this chapter. Also it contains the definition of the class . Section 3.2, subordination, superordination and sandwich-type theorems for are obtained. Section 3.3, subordination and superordination results for are obtained. Section 3.4, subordination results for the class are obtained. Remarks 2. (i) The results of Section 3.2 have been published in J. Inequal. Appl. ( see [13]); (ii) The results of Section 3.4 have been published in Indian J. Math. ( see [11]). Chapter 4 consists of three sections. Section 4.1, is an introductory section contains some primary lemmas which we will need to obtain our results and the definition of the operator . Section 4.2, differential subordination and superordination results for analytic p-valent functions defined by the operator are obtained. Section 4.3, subordination, superordination and sandwish results for analytic p-valent functions defined by the operator are obtained. Remarks 3. The contents of Section 4.2 have been published in Int. J. Open Problems Complex Analysis (see [12]). Chapter 5 consists of four sections. Section 5.1, is an introductory section contains some primary lemmas which we will need to obtain our results and the definitions of the operators , also the definition of the class . Section 5.2, some inclusion relations for subclasses of p-valent functions involving the operator are obtained. Section 5.3, some inclusion relations for subclasses of p-valent functions involving the operator are obtained.Section 5.4, a note on subclass of analytic functions defined by the operator is obtained. Remarks 4. The contents of Section 5.2 have been accepted for publication in Acta Univ. Apulensis ( see [14] ). |