Sürekli ve türevlenebilir fonksiyonlara yaklaşan bazı genelleştirilmiş pozitif operatörler

Abstract

This thesis consist of five chapters. The first chapter is divided differences, convex functions, linear positive operators, P.P. Korovkin theorem on C(a,b) spaces, Bernstein polynomials and characteristics. The second, third, fourth and fifth chapters are the original parts of the study. In the second chapter, generalization of Bernstein polynomials are defined and approximation of continuous functions are given. In the third chapter, monotonicity of Bernstein polynomials are given. In the fourth chapter, some numerical methods are given for the solutions of some differential equations. In the fifth chapter, generalization of Sasz operators are given. KEY WORDS: Bernstein polynomials, Linear positive operators, Convex functions, Divided differences, Sasz operators.