Hyers-Ulam stability of K-Fibonacci functional equation

Document Type : Research Paper

Authors

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 $F_{k,n} = kF_{k,n-1}+ F_{k,n-2}$ for $n\geq 2$ 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

Volume 2, Issue 1 - Serial Number 1
January 2011
Pages 42-49
  • Receive Date: 21 January 2010
  • Revise Date: 04 June 2010
  • Accept Date: 19 June 2010