Author:
Han Jeong Soon,Kim Hee Sik,Neggers Joseph
Abstract
Abstract
In this paper we consider Fibonacci functions on the real numbers R, i.e., functions
f
:
R
→
R
such that for all
x
∈
R
,
f
(
x
+
2
)
=
f
(
x
+
1
)
+
f
(
x
)
. We develop the notion of Fibonacci functions using the concept of f-even and f-odd functions. Moreover, we show that if f is a Fibonacci function then
lim
x
→
∞
f
(
x
+
1
)
f
(
x
)
=
1
+
5
2
.
MSC:11B39, 39A10.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference6 articles.
1. Atanasov K, et al.: New Visual Perspectives on Fibonacci Numbers. World Scientific, Hackensack; 2002.
2. Dunlap RA: The Golden Ratio and Fibonacci Numbers. World Scientific, Hackensack; 1997.
3. Han JS, Kim HS, Neggers J: The Fibonacci norm of a positive integer n -observations and conjectures. Int. J. Number Theory 2010, 6: 371–385. 10.1142/S1793042110003009
4. Han JS, Kim HS, Neggers J: Fibonacci sequences in groupoids. Adv. Differ. Equ. 2012., 2012:
5. Jung SM: Hyers-Ulam stability of Fibonacci functional equation. Bull. Iran. Math. Soc. 2009, 35: 217–227.
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