Lineer olmayan singüler integral operatorlerinin bir sınıfının yaklaşım özellikleri

This thesis is a survey on some approximation properties of nonlinear singular integraloperators in the approximation theory. One of the fundamental problems ofanalysis is to approximate a given function f in some sense or other by functions havingcertain properties, and generally, by functions which have ?better? properties thanf . It is to be expected that the better behaved functions are to be constructed from thegiven f by some smoothing operation on f itself.This thesis consists of five chapters. The first chapter is devoted to the introduction.The second chapter contains concepts, definitions and also some fundamental informationsabout Stieltjes integral and bounded variations, which we need further studies andcalculations. In the third chapter, we give some informations about the approximationproblem and some important inequalities with their proofs. In chapter four, we studythe pointwise convergence and the rate of pointwise convergence of nonlinear singularintegrals by considering different functional spaces. In the last chapter, we give someexamples of kernels of the mentioned the nonlinear singular integral operators.