الفهرس 
Univalent functionsOnly 14 pages are availabe for public view
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Abstract
In this thesis, some studies of the well known properties of the geometric function theory has introduced on comprehensive generating subclasses of the class of analytic functions, which some of its members de
ned on the unit open disc U and the other de
ned on the punctured disc U , to have an image located in the real part of the complex plane C. Using some various operators and subordination principle, these de
ned subclasses is investigated. Also, di
erent analytic and geometric properties of the functions belonging to each subclass are introduced. At the end of each chapter, several connections to some of the earlier results are pointed out. In a brief, the contents of each chapter is presented as follow: Chapter One: Some notation and standard de
nitions of univalent, multivalent, meromorphic and bi-univalent functions are introduced. Also, several subclasses of generalized geometric functions and historical notes about studies corresponding to them are pointed out. Also, important problems related Hankel determinant and Fekete Sezgo are introduced. Finally, some linear operators used during this thesis are established. Chapter Two: A new modi
ed Salagean operator is investigated utilizing the q-di
erence operator. Making use of that operator, new extensive classes of starlike and convex function Tp;q(n; j;
; A;B) and Cp;q(n; j;
; A;B) are investigated. Also, some of important properties of geometric function theory (as mentioned but a few, Coe
cient Estimation, Distortion Bounds ... etc) is presented. Finally, several application on the q-fraction calculus in the functions belonging to these subclasses are obtained. The results of this chapter is published at the journal Transactions of A. Razmadze Mathematical Institute, volume (172), 2018. iv Preface Chapter Three: In the light of the q-analogue theory, the inclusion relationships involving (
; p; j; q)-neighborhoods and some integral means inequalities corresponding to the functions belonging to the pre-mentioned classes Tp;q(n; j;
; A;B) and Cp;q(n; j;
; A;B), which introduced in the
rst chapter, are investigated. Also, some integral operators de
ned on the family of multivalent meromorphic functions p are obtained and whence several subfamilies of multivalent meromorphic functions are established. Various inclusion relationships and integral-preserving properties are investigated. Some results of this chapter is published at the journal Acta Universitatis Apulensis, volume (59), 2019. Chapter Four: Comprehensive subclasses of bi-univalent analytic functions are presented. Estimation of the upper bound of the initial Tayler-Maclaurin coe
cients and the Fekete-Szego inequalities of functions belonging to these subclasses are investigated as our main Theorems. At the end of this chapter, varies connections to some of the previous known results are pointed out. Some results of this chapter is published at the journal Journal of the Egyptian Mathematical Society, volume (27), 2019. Chapter Five: This chapter is concerning on giving an estimation of the upper bound of the modulus of Tayler-Maclaurin coe
cients an (n 2 Nf1g) by using the Faber polynomials. First, a subspace of the space of the biunivalent analytic functions are introduced. Then, the target estimations are determined. Also, a special form of the Fekete-Szego functional of the pre-mentioned subspaces is estimated. Also, the upper bound of the second Hankel determinant jH2(2)j = ja2a4 a23 j of these subspaces is obtained. Finally, some new results is presented as particular cases of our main results.