Meyer-König ve Zeller operatörleri üzerine

This thesis is a survey on Meyer-König and Zeller operators which are well-known positive linear operators in the approximation theory.This thesis consists of four chapters. In the first chapter, a short history of thestudies on the approximation of the linear positive operators, and some basic definitions and theorems are given. In the second chapter, some approximation properties of a generalization of Meyer-König and Zeller operators via generating functions and a Kantarovich type generalization of Meyer-König and Zeller operators are obtained. Also, the rate of convergence of these operators, with the help of usual modulus of continuity and the elements of Lipschitz class, is computed and an application to functional differential equations is presented. In the third chapter, explicit formulas and some estimates for the moments of Meyer-König and Zeller operators are given. In the final chapter, it is shown that Meyer-König and Zeller operators preserve the Lipschitz constants and satisfy an initial value problem.