Lineer olmayan bernstein tipi operatörler ve onların yaklaşım özellikleri

This thesis deals with approximation properties of certain nonlinear Bernstein type operators in the approximation theory. This thesis consists of four chapters. The first chapter is devoted to the introduction. The second chapter contains concepts, definitions and also some important inequalities which are needed in the further chapters. In the third chapter, after giving some information about the nonlinear singular integral operators, existence theorem for these operators are investigated. Moreover, Fatou type convergence properties of the derivatives of these operators are studied. Then, convergence of the nonlinear Bernstein type operators are examined and using the modulus of continuity, the rate of convergence of these operators are investigated. Furthermore, by means of this operators, the pointwise convergence on some specified points are studied. Then, their pointwise convergence to some functions which are derivatives of bounded variation are observed. Finally, a Voronovskaya type formula is provided for nonlinear Bernstein type operators. In the last chapter, conclusion of the thesis and some recommendations for further studies can be found.