Investigation of the Properties of a New Class of Interpolation Polynomials Based on Fibonacci Numbers

In this paper, a class of new polynomials based on Fibonacci sequence using Newton interpolation is introduced. This target is performed once using Newton forward- divided- difference formula and another more using Newton backward- divided- difference formula. Some interesting results are obtained for forward and backward differences. The relationship between forward (and backward) differences and the Khayyam- Pascal’s triangle are also examined.