On Fibonacci Functions with Period k

Abstract EN

A function f:ℝ→ℝ is said to be a Fibonacci function if f(x+2)=f(x+1)+f(x) for all x∈ℝ.

In 2012, some properties on the Fibonacci functions were presented.

In this paper, for any positive integer k, a function f:ℝ→ℝ is said to be a Fibonacci function with period k if f(x+2k)=f(x+k)+f(x) for all x∈ℝ; we present some properties on the Fibonacci functions with period k.