On Fibonacci functions with Fibonacci numbers
Copyright policy )On Fibonacci functions with Fibonacci numbers
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.
- University of Alabama, USA United States
- Hanyang University Korea (Republic of)
- University of Alabama System United States
- Alabama Agricultural and Mechanical University United States
- Hanyang University Korea (Republic of)
Algebra and Number Theory, Applied Mathematics, Functions of bounded variation, generalizations, Fibonacci and Lucas numbers and polynomials and generalizations, Fibonacci function, golden ratio, Analysis, \(f\)-even (\(f\)-odd) function
Algebra and Number Theory, Applied Mathematics, Functions of bounded variation, generalizations, Fibonacci and Lucas numbers and polynomials and generalizations, Fibonacci function, golden ratio, Analysis, \(f\)-even (\(f\)-odd) function
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