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In this paper we consider Fibonacci functions on the real numbers R, i.e., functions f : 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; 39A10doi:10.1186/1687-1847-2012-126 fatcat:ndgoc4kftnhcxchwxpiuaplflu