Mamedov tipli m-singüler i̇ntegral operatörler ve onların yakınsaklık özellikleri

This thesis is a survey on some approximation properties of Mamedov type m- singular integral operators in the approximation theory. One of the fundamental problems of analysis is to approximate a given function f in some sense or other by functions having certain properties, and generally, by functions which have `better' properties than f. It is to be expected that the better behaved functions are to be constructed from the given f by some smoothing operation on f itself. This thesis consists of five chapters. The fi rst chapter is devoted to the introduction. The second chapter contains concepts, de finitions and also some important theorems, which we need further studies and calculations. In the third chapter, we give some informations about the modulus of continuity and we give Approximation problem.In the fourth chapter, we study m-singular integral operators and m-th modulus of smoothness and rate of convergence of m-singular integral operator on (p,m)-Lebesgue point and ( \mu,p,m)-Lebesgue point. Finally in the last chapter we study Mellin type nonlinear m-singular integral operators and its pointwise convergence.