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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 45 Issue: 2

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

Julius Fergy Tiongson Rabago
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Yayın Tarihi
2016-04-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let w be a real-valued function on R and k be a positive integer.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Second-order linear recurrent functions with period k · Horadam numbers · generalized Fibonacci sequences

Abstract

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.

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Bu Makaleye Atıf Yap

Rabago, J. F. T. (2016). On second-order linear recurrent functions with period k and proofs to two conjectures of Sroysang. Hacettepe Journal of Mathematics and Statistics, Volume: 45 Issue: 2. https://ajindex.com/articles/1403170

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Kaynakça (21)

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