Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68222120110101Hyers-Ulam stability of K-Fibonacci functional equation42499510.22075/ijnaa.2011.95ENM. BidkhamDepartment of Mathematics, Semnan University, P. O. Box 35195-363, Semnan,
Iran.M. HosseiniDepartment of Mathematics, Semnan University, P. O. Box 35195-363, Semnan,
Iran.Journal Article20101221Let denote by Fk,n the nth k-Fibonacci number where Fk,n = kFk,n−1+<br />Fk,n−2 for n 2 with initial conditions Fk,0 = 0, Fk,1 = 1, we may derive a functional<br />equation f(k, x) = kf(k, x − 1) + f(k, x − 2). In this paper, we solve this<br />equation and prove its Hyere-Ulam stability in the class of functions f : N×R ! X,<br />where X is a real Banach space.https://ijnaa.semnan.ac.ir/article_95_e74695e8f1e27bdde3cc846ede0714d7.pdf