Darwish, Hanan Elsied AwadShahen, Awatef Abd ElganyAL-Mutairi, Norah Saud Dhaifallah2024-09-102024-09-102024https://hdl.handle.net/20.500.14154/73028Chapter 1 This chapter is an introductory chapter and contains basic concepts, definitions and preliminary results which are absolutely essential for completing the results and techniques used in subsequent chapters. Chapter 2. In this chapter there are two sections Section 1 In this section subordination, superordination and sandwich theorems are established for a class of p-valent analytic functions involving a generalized integral operator that has as special case p-valent Sălăgean integral operator. Relevant connections of the new results with several well-known ones are given as a conclusion for this investigation. Section 2 This section presents a novel investigation that utilizes the integral operator I_(p,λ)^n in the field of geometric function theory, with a specific focus on sandwich theorems. The student obtained findings about the differential subordination and superordination of a novel formula for a generalized integral operator. Additionally, certain sandwich theorems were discovered. Chapter 3. In this Chapter, the student examines a novel category of analytic and bi-univalent functions that are linked to q-Srivastava-Attiya in the open unit disk. By establishing coefficient boundaries, it is possible to obtain the Taylor-Maclaurin coefficients |a_2 | and |a_3 | of the functions from these recently introduced subcategories. Furthermore, the student establish the Fekete-Szegö inequality for functions in the classes T_(τ,q,α)^ϵ (ψ),kH_(τ,q,α)^ϵ (δ,ψ),A_(τ,q ,α)^ϵ (δ,ψ). Chapter 4. In this chapter, the new generalized classes of (p,q)- starlike and (p,q)- convex functions are introduced by using the (p,q)-derivative operator. Certain subclasses of analytic univalent functions associated with quasi-subordination are defined and the bounds for the Fekete-Szegö coefficient functional |a_3-μ a_2^2 | for functions belonging to these subclasses are derived. Chapter 5. In this chapter, using the q-Difference operator, the student developed a subclass of meromorphically p-valent functions with alternating coefficients. Additionally, the student obtained multivalent function convolution results and coefficient limits. Chapter 6. In this chapter there are two sections Section 1. This section defines a new class of meromorphic parabolic starlike functions in the punctured unit disc that includes fixed second coefficients of class A_(s,c)^d (ψ,τ,ν,η)and the q-hypergeometric functions. For the function belonging to the class A_(s,c)^d ( ψ ,τ,ν,η), some properties are obtained, including the coefficient inequalities, closure theorems, and the radius of convexity. Section 2. In this section, the student introduces a new class of applications of the q-Srivastava-Attiya operator involving a certain family of univalent functions with many fixed coefficients defined in the open unit disk. By making use of the q-Srivastava- Attiya operator J_(q,t)^(s ). Properties like coefficient condition, radii of starlikeness and convexity, extreme points and integral operators applied to functions in the class are investigated.In this thesis, the student introduces new classes of analytic functions defined by using some differential and integral operators and the Hadamard product in the open unit disc and study various properties of these classes. This thesis mainly of six chapters.159enAnalytic Functionsوsubordinationsuperordinationsandwich theoremsThesis