Bernstein-Chlodowsky type polynomials and some applications

This thesis consists of four chapters. The aim of this thesis is to give the relations of Bernstein Chlodowsky polynomials in analytic number theory. In the first chapter, definitions and theorems that will constitute the background of the thesis are given. In the second chapter, Bernstein polynomial which is the basis of Bernstein-Chlodowsky polynomials which are the main subject of the thesis and necessary theorems are given and their properties are presented. In the third chapter, the reason for the output of Bernstein-Chlodowsky polynomial, the needs of the polynomial, the answers to the needs and the necessary important theorems are shown. In the last chapter, the generating function of q- Bernstein-Chlodowksy polynomials is defined and the fundamental properties of these polynomials are investigated. In addition, by making use of fermionic p- adic integral and q- Volkenborn integral, the relations for q- Bernstein-Chlodowsky polynomials with weighted q- Euler and q- Bernoulli numbers are found.