**Thesis Type:** Post Graduate

**Institution Of The Thesis:** Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey

**Approval Date:** 2015

**Student:** PELİN KARATAŞLI

**Consultant: **OGÜN DOĞRU

This thesis in which a generalization of q-Balazs-Szabados operators is introduced and the approximation properties of these operators are investigated, first of all, Korovkin theorem is proved; definitions of Balazs and Balazs-Szabados operators are given, some properties of these operators are investigated and q-analogue of Balazs Szabados operators and some related concepts are introduced. After that, Korovkin type approximation properties of q- Balazs-Szabados operators are investigated via Korovkin theorem; the definition of modulus of continuity and some features of it are given and rate of convergence of q- Balazs-Szabados operators are obtained via modulus of continuity. Moreover, two- variable q-Balazs-Szabados operators are defined and some properties of them are investigated via Volkov theorem. Finally, approximation properties of bivariate q-Balazs- Szabados operators are investigated via modulus of continuity.