Approximation Properties of Schurer Type q-Bernstein Operators

This thesis consist of five chapters. In the first chapter, the introduction is given. In the second chapter, we consider the Chlodowsky variant of q-Bernstein-Schurer-Stancu operators. We state the Korovkin type approximation theorem and obtain the error of approximation by using modulus of continuity and Lipschitz-type functionals. Moreover, we obtain the rate of approximation in terms of the first derivative of the function and we examine the generalization of the operators. In the third chapter, we define Chlodowsky type q-Bernstein-Stancu-Kantorovich operators. Many properties and results of these polynomials, such as Korovkin type approximation and the rate of convergence of these operators in terms of Lipschitz class functional are given. In the fourth chapter, we introduce and study Chlodowsky-Durrmeyer type q-Bernstein- Schurer-Stancu operators. We state the Korovkin-type approximation theorem and obtain the order of convergence of the operators. In the last chapter, we define two dimensional Chlodowsky type of q-Bernstein-Schurer- Stancu operators. We study Korovkin-type approximation theorem and state the error of approximation by using full and partial modulus of continuity. Finally, we define the generalization of the operators and investigate their approximation properties in weighted space. Keywords: Chlodowsky variant of q-Bernstein-Schurer-Stancu operators, Chlodowsky type q-Bernstein-Stancu-Kantorovich, Chlodowsky-type q-Durrmeyer operators.