Approach of functions with rational functions in some function classes

In this study, firstly, the direct theorem about the approximation of the continuous functions defined on closed regular curves by the sequence of rational functions is obtained. In addition, information about the derivative of the sequence of rational functions is given. In quasiconform curves, the inverse of the theorem is obtained. The approximation problem has been investigated in terms of the 2nd integral modulus of continuity by Faber-Laurent rational functions in weighted Lebesgue spaces defined on kuasi-smooth closed Jordan curves. Then, the approximation of continuous functions defined on the closed quasiconform curve by Faber-Laurent rational functions is examined. The results are obtained in terms of the functions best approximation. Also, in this thesis, the class of local functions is defined. In quasiconform curves, the direct local theorem regarding the approximation of continuous functions by rational functions is obtained.