Research Information System
Thesis Type: Doctorate
Institution Of The Thesis: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey
Approval Date: 2020
Thesis Language: Turkish
Student: SEMRA KUŞ
Supervisor: NAİM TUĞLU
Open Archive Collection: AVESIS Open Access Collection
Abstract:In this thesis, a new F-exponential generating function for Bernoulli F−polynomials and various properties of Bernoulli F−polynomials are obtained. By identifying Euler-Fibonacci numbers and polynomials, F-exponential generating function of these polynomials are found. In addition, the relationship of Euler-Fibonacci numbers and polynomials with Bernoulli F−polynomials is shown. Then, harmonic based F-exponential function is defined. Harmonic based F-exponential generating function is defined for Bernoulli F−polynomials, Euler-Fibonacci numbers, Euler-Fibonacci polynomials and Bernoulli-Fibonacci numbers, and their relations are shown with harmonic Fibonacci numbers and polynomials. The Fibo-Bernoulli matrix is defined using Bernoulli F−polynomials. The generalized Fibo-Pascal matrix is multiplied by a special matrix with fibonomial coefficient to obtain the Fibo-Bernoulli matrix. Also the inverse of the Fibo-Bernoulli matrix is found. Finally, Fibo-Euler matrices are defined and their relation with Fibo-Bernoulli matrix is shown.