Bernstein polynomial's applications


Thesis Type: Postgraduate

Institution Of The Thesis: Uludağ Üniversitesi, Turkey

Approval Date: 2011

Thesis Language: Turkish

Student: ELİF ÇETİN

Supervisor: İSMAİL NACİ CANGÜL

Abstract:

In this work, Bernstein polynomials are defined and from using the several properties of Bernstein polynomials which are given before, some new results about Bernstein polynomias are found. The thesis consists of four chapters. In the first chapter, the preliminary notions which are to be used in later chapters are given. Besides, Gamma and Beta functions are defined and some basic properties of these functions are given. In the second chapter, Bernstein polynomials are defined and the basic properties about Bernstein polynomials are given. In the third chapter, firstly the integral of the Bernstein polynomials are investigated and then, the integral of the multiplication of the Bernstein polynomials are given. Besides, Bernstein polynomials relations with Gamma and Beta functions are given. In the fourth chapter which is the last one, from a basic property of the derivative of Bernstein polynomials, firstly generalization of the derivative of Bernstein polynomials are given. After that, some new results are inspired from the third chapter, which is about the multiplication of the derivation of Bernstein polynomials.