Let denote by Fk,n the nth k-Fibonacci number where Fk,n = kFk,n−1+ Fk,n−2 for n 2 with initial conditions Fk,0 = 0, Fk,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 : N×R ! 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. doi: 10.22075/ijnaa.2011.95
MLA
M. Bidkham; M. Hosseini. "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
VANCOUVER
Bidkham, M., Hosseini, M. Hyers-Ulam stability of K-Fibonacci functional equation. International Journal of Nonlinear Analysis and Applications, 2011; 2(1): 42-49. doi: 10.22075/ijnaa.2011.95
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