@article {
author = {Bidkham, M. and Hosseini, M.},
title = {Hyers-Ulam stability of K-Fibonacci functional equation},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {2},
number = {1},
pages = {42-49},
year = {2011},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2011.95},
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 = {stability,Fibonacci functional equation},
url = {https://ijnaa.semnan.ac.ir/article_95.html},
eprint = {https://ijnaa.semnan.ac.ir/article_95_e74695e8f1e27bdde3cc846ede0714d7.pdf}
}