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 ∈ 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.
关键词：Fibonacci function ; f -even ( f -odd) function ; Golden ratio
