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.
Bidkham, M. & Hosseini, M. (2011). Hyers-Ulam stability of K-Fibonacci functional equation. International Journal of Nonlinear Analysis and Applications, 2(1), 42–49. https://doi.org/10.22075/ijnaa.2011.95
MLA
Bidkham, M., & Hosseini, M. "Hyers-Ulam stability of K-Fibonacci functional equation", International Journal of Nonlinear Analysis and Applications, 2, 1, 2011, 42–49. doi: 10.22075/ijnaa.2011.95
HARVARD
Bidkham, M., & Hosseini, M. (2011). 'Hyers-Ulam stability of K-Fibonacci functional equation', International Journal of Nonlinear Analysis and Applications, 2(1), pp. 42–49. doi: 10.22075/ijnaa.2011.95
CHICAGO
Bidkham, M. & Hosseini, M., "Hyers-Ulam stability of K-Fibonacci functional equation." International Journal of Nonlinear Analysis and Applications, 2 1 (2011): 42–49, doi: 10.22075/ijnaa.2011.95
VANCOUVER
Bidkham M., Hosseini M. Hyers-Ulam stability of K-Fibonacci functional equation. IJNAA. 2011;2(1):42–49. doi: 10.22075/ijnaa.2011.95
International Journal of Nonlinear Analysis and Applications