Generalized Golden-Fibonacci calculus and applications
tarafından
 
Özvatan, Merve, author.

Başlık
Generalized Golden-Fibonacci calculus and applications

Yazar
Özvatan, Merve, author.

Yazar Ek Girişi
Özvatan, Merve, author.

Fiziksel Tanımlama
viii, 152 leaves:+ 1 computer laser optical disc.

Özet
In the present thesis the Golden-Fibonacci calculus is developed and several applications of this calculus are obtained. The calculus is based on the Golden derivative as a finite difference operator with Golden and Silver ratio bases, which allowed us to introduce Golden polynomials and Taylor expansion in terms of these polynomials. The Golden binomial and its expansion in terms of Fibonomial coefficients is derived. We proved that Golden binomials coincide with Carlitz’ characteristic polynomials. By Golden Fibonacci exponential functions and related entire functions, the Golden-heat and the Golden-wave equations are introduced and solved. By introducing higher order Golden Fibonacci derivatives, related with powers of golden ratio, we develop the higher order Golden Fibonacci calculus. The higher order Fibonacci numbers, higher Golden periodic functions and higher Fibonomials appear as ingredients of this calculus. By using Golden Fibonacci exponential function, we introduce the generating function for new type of polynomials, the Bernoulli-Fibonacci polynomials and study their properties. As a geometrical application, the Apollonious type gaskets are described in terms of Fibonacci, Lucas and generalized Fibonacci numbers. Some mod 5 congruencies associated with Fibonacci and Lucas numbers are obtained.

Konu Başlığı
Fibonacci numbers.

Yazar Ek Girişi
Pashaev, Oktay,

Tüzel Kişi Ek Girişi
İzmir Institute of Technology. Mathematics.

Tek Biçim Eser Adı
Thesis (Master)--İzmir Institute of Technology: Mathematics.
 
İzmir Institute of Technology: Mathematics--Thesis (Master).

Elektronik Erişim
Access to Electronic Versiyon.


LibraryMateryal TürüDemirbaş NumarasıYer NumarasıDurumu/İade Tarihi
IYTE LibraryTezT001790QA241 .O99 2018Tez Koleksiyonu