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 6 条

[1]

Atanasov K., 2002, NEW VISUAL PERSPECTI

[2]

Dunlap R.A., 1997, GOLDEN RATIO FIBONAC

[3] Fibonacci sequences in groupoids [J].

Han, Jeong Soon ;

Kim, Hee Sik ;

Neggers, Joseph .

ADVANCES IN DIFFERENCE EQUATIONS, 2012,

[4] THE FIBONACCI-NORM OF A POSITIVE INTEGER: OBSERVATIONS AND CONJECTURES [J].

Han, Jeong Soon ;

Kim, Hee Sik ;

Neggers, J. .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2010, 6 (02) :371-385

[5]

Jung SM, 2009, B IRAN MATH SOC, V35, P217

[6] Fibonacci mean and golden section mean [J].

Kim, Hee Sik ;

Neggers, J. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (01) :228-232

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