On Fibonacci functions with Fibonacci numbers

被引：9

作者：

Han, Jeong Soon ^{[1
]}

Kim, Hee Sik ^{[2
]}

Neggers, Joseph ^{[3
]}

机构：

[1] Hanyang Univ, Dept Appl Math, Ahnsan 426791, South Korea

[2] Hanyang Univ, Dept Math, Res Inst Nat Sci, Seoul 133791, South Korea

[3] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2012年

关键词：

Fibonacci function; f-even (f-odd) function; Golden ratio;

D O I：

10.1186/1687-1847-2012-126

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider Fibonacci functions on the real numbers R, i.e., functions f : R -> R such that for all x is an element of R, f(x + 2) = f(x + 1) + f(x). We develop the notion of Fibonacci functions using the concept of f f-even and f-odd functions. Moreover, we show that if f is a Fibonacci function then lim(x ->infinity) f(x+1)/f(x) = 1+root 5/2.

引用

页数：7

共 50 条

[31] NOTE ON SOME ARITHMETIC FUNCTIONS CONNECTED WITH FIBONACCI NUMBERS
VAUGHAN, TP
FIBONACCI QUARTERLY, 1976, 14 (03): : 244 - 248
[32] The continuous functions for the Fibonacci and Lucas p-numbers
Stakhov, A
Rozin, B
CHAOS SOLITONS & FRACTALS, 2006, 28 (04) : 1014 - 1025
[33] Equations involving arithmetic functions of Fibonacci and Lucas numbers
Luca, F
FIBONACCI QUARTERLY, 2000, 38 (01): : 49 - 55
[34] Average of the Fibonacci Numbers
Fatehizadeh, Amirali
Yaqubi, Daniel
JOURNAL OF INTEGER SEQUENCES, 2022, 25 (02)
[35] COMPLEX FIBONACCI NUMBERS
HARMAN, CJ
FIBONACCI QUARTERLY, 1981, 19 (01): : 82 - 86
[36] FIBONACCI NUMBERS IN DIATOMS
BROUSSEAU, A
FIBONACCI QUARTERLY, 1977, 15 (04): : 370 - 370
[37] ON THE RECIPROCALS OF THE FIBONACCI NUMBERS
HOCHWALD, SH
TONG, JC
FIBONACCI QUARTERLY, 1993, 31 (03): : 246 - 250
[38] HYPERSPACES AND FIBONACCI NUMBERS
HAASE, H
FIBONACCI QUARTERLY, 1993, 31 (02): : 158 - 161
[39] The (Fabulous) Fibonacci Numbers
Miocevic, Ljubica
EUROPEAN LEGACY-TOWARD NEW PARADIGMS, 2010, 15 (01): : 109 - 110
[40] L-FUNCTIONS OF ELLIPTIC CURVES AND FIBONACCI NUMBERS
Luca, Florian
Yalciner, Aynur
FIBONACCI QUARTERLY, 2013, 51 (02): : 112 - 118

← 1 2 3 4 5 →