Document Type : Research Paper

Authors

• M. Bidkham
• M. Hosseini

Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.

Abstract

Let denote by $F_{k,n}$ the $n^{th}$ $k$-Fibonacci number where $F_{k,n}=k{F}_{k,n-1}+F_{k,n-2}$ for $n\ge 2$ with initial conditions $F_{k,0}=0,F_{k,1}=1$, we may derive a functional equation $f(k,x)=kf(k,x-1)+f(k,x-2)$. In this paper, we solve this equation and prove its Hyere-Ulam stability in the class of functions $f:\mathbb{N}\times \mathbb{R}\to X$, where $X$ is a real Banach space.

Keywords

• stability
• Fibonacci functional equation