Approximation by q- bernstein -chlodowsky polynoms

This dissertation includes four chapters. In the first chapter, the general properties of various function spaces and linear positive operators, some approximation theorems for these function spaces and some elementary definitions and theorems which are used throughout the thesis are given. In the second chapter; firstly the approximation properties for Bernstein polynomial of one variable and Bernstein polynomial of two variables are examined. And then the approximation properties for Bernstein –Chlodowsky polynomials of one variable, two and three variables are considered. Finally, approximation of Bernstein –Chlodowsky polynomials of two and three variables are visualized by means of graphs. In the third chapter; first of all, primary definitions and theorems of q -Analysis are given. And then approximation properties of q -Bernstein polynomials of one variable and two variables are examined. The approximation properties of q -Bernstein –Chlodowsky polynomials of two and three variables are tackled by using a similar way to the second chapter. In addition to this, the approximation process are plotted. In the last chapter, the approximation speed of Bernstein and q -Bernstein polynomials of one variable and two variables are studied with the help of modulus of continuity and weighted modulus of continuity. In addition to this, the approximation speed of Bernstein –Chlodowsky polynomials of two and three variables and the approximation speed of q -Bernstein –Chlodowsky polynomials are investigated via modulus of continuity and weighted modulus of continuity in similar way.