On Fibonacci functions with period \(k\) (Q1956053)

Summary: A function \(f : \mathbb R \to \mathbb R\) is said to be a Fibonacci function if \(f(x + 2) = f(x + 1) + f(x)\) for all \(x \in \mathbb R\). In 2012, some properties on the Fibonacci functions were presented. In this paper, for any positive integer \(k\), a function \(f : \mathbb R \to \mathbb R\) is said to be a Fibonacci function with period \(k\) if \(f(x + 2k) = f(x + k) + f(x)\) for all \(x \in \mathbb R\); we present some properties on the Fibonacci functions with period \(k\).