Reflections of Fibonacci calculus on some number sequences and polynomials

This thesis consists of six chapters. In the first part of the thesis, the introduction and definitions that will be required throughout the thesis are included. In the second part of the thesis, basic definitions, theorems and identities for the Fibonacci number sequence are included. In the third part of the thesis basic definitions, theorems and identities regarding the Bernstein operator and Bernstein polynomials are included. In the fourth chapter of the thesis basic definitions, theorems and identities of Bernoulli numbers and polynomials and Euler numbers and polynomials are included. In the fifth chapter of the thesis definitions, theorems and identities related to Bernoulli F-polynomial, Bernoulli-Fibonacci numbers and polynomials, Euler-Fibonacci numbers and polynomials, F-Bernstein operator and F-Bernstein polynomial are included. In the sixth chapter of the thesis the findings and conclusions are included.