Blending Type Bernstein Operators

The aim of my thesis is to examine the Bernstein Operators, which are linear positive operators and the properties of the New Generalized Operators. My thesis consists of four parts. The first part is an introduction and gives information about the parts that we will examine in the following chapters. The second chapter is to give more information about all the fundamental theorems and properties. In this section, the basic theorems used in the thesis are proved and explained with examples. In the third part, Korovkin Theorem’s proof and Bernstein Operators and approximation propeties and converges uniformly of Bernstein operators are given. In the last, new family of generalized Bernstein operators' definition and some important theory of convergence approximation of functions are given. After that we will examine some important results regarding the rate of converges and predictions of new generelized operators, that are appliactions of the properties and formulas which are foretold. Lastly, we examine the shape preservation properties and complete the thesis.