**Thesis Type:** Postgraduate

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

**Approval Date:** 2017

**Thesis Language:** Turkish

**Student:** ZELİHA KARAHÜSEYİN

**Supervisor: **Sibel Yalçın Tokgöz

This thesis consist of four chapters. In the first chapter; some definitions and theorems about analytic functions which will be used later are introduced. Furthermore, some properties related to q-calculus and q-derivative are given. In the second chapter; basic properties related to the classes analytic and univalent functions in U are given. In the third chapter; the some special subclasses of analytic univalent functions defined by q-derivative operator are worked and coefficient estimates are given for functions in these classes. In addition, theorems for these classes were examined. In the fourth chapter; all obtained results are discussed.