Statistical Korovkin type approximation theorems

This thesis consists of three chapters. The first chapter has been devoted to theintroduction. In the second chapter, statistical convergence has been recalled. Examplesand some results concerning this concept has been given. In the first section of the thirdchapter some general information about positive linear operators and in the secondsection classical Korovkin type theorems have been given. In the third section usingstatistical convergence Korovkin type theorem has been studied and the order of thistheorem has been given. In the fourth and fifth sections statistical Korovkin typetheorem for periodic functions and statistical Korovkin type theorem in [ , ] p L a b havebeen considered, respectively. In the last section equi-statistical convergence of positivelinear operators and using equi-statistical convergence Korovkin type theorem studied.Then, an example such that this theorem works but its classical and statistical cases donot work has been given. Also, the rates of equi-statistical convergence have beencomputed.Key Words: Statistical convergence, positive linear operator, Korovkin typeapproximation theorem, statistical uniform convergence,modulus of continuity, equistatisticalconvergence.