On second-order linear recurrent functions with period k and proofs to two conjectures of Sroysang

Julius Fergy Tiongson RABAGO

Makale detayları

On second-order linear recurrent functions with period k and proofs to two conjectures of Sroysang

Yazarlar:

Julius Fergy Tiongson RABAGO

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2016 Vol.45 Issue 2, pp.429-446

Belge Tipi:

Makale

Yayın Tarihi:

3/2016

Belge Dili:

İngilizce

Document ID (Org No.):

2000452694

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

Özet:

 

Let w be a real-valued function on R and k be a positive integer. If
for every real number x, w(x + 2k) = rw(x + k) + sw(x) for some nonnegative real numbers r and s, then we call such function a second-order
linear recurrent function with period k. Similarly, we call a function
w : R → R satisfying w(x + 2k) = −rw(x + k) + sw(x) an odd secondorder linear recurrent function with period k. In this work, we present
some elementary properties of these type of functions and develop the
concept using the notion of f-even and f-odd functions discussed in [9].
We also investigate the products and quotients of these functions and
provide in this work a proof of the conjecture of B. Sroysang which he
posed in [19]. In fact, we offer here a proof of a more general case of the
problem. Consequently, we present findings that confirm recent results
in the theory of Fibonacci functions [9] and contribute new results in
the development of this topic.

Makale detayları

On second-order linear recurrent functions with period k and proofs to two conjectures of Sroysang

Yazarlar: Julius Fergy Tiongson RABAGO

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2016 Vol.45 Issue 2, pp.429-446

Belge Tipi: Makale

Yayın Tarihi: 3/2016

Belge Dili: İngilizce

Document ID (Org No.): 2000452694

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

Sayı

Yazarlar:

Julius Fergy Tiongson RABAGO

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2016 Vol.45 Issue 2, pp.429-446

Belge Tipi:

Makale

Yayın Tarihi:

3/2016

Belge Dili:

İngilizce

Document ID (Org No.):

2000452694

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X