Concave univalent functions


Thesis Type: Doctorate

Institution Of The Thesis: Bursa Uludağ University, Fen Bilimleri Enstitüsü, Mathematics, Turkey

Approval Date: 2019

Thesis Language: Turkish

Student: HASAN BAYRAM

Supervisor: Sibel Yalçın Tokgöz

Abstract:

This thesis consist of four chapters. The aim of this thesis is to examine concave univalent functions and to define new classes. In the first chapter; some of definitions and theorems which will be used later are introduced. In the second chapter; the basic features of the S class which is composed of normalized analytical and univalent functions, are given in the open unit disk D. Furthermore the coefficient equations, theorems of the growth, covering and distortion results for univalent functions were examined. In the third section, which constitutes the main part of the thesis, the definition of classes of concave univalent functions and some special subclasses and theorems of these classes were defined. In addition, some concave univalence criteria were examined. In the last section, a general review of the thesis was made.