International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 4, Pages 217-229
doi:10.1155/S0161171201004707
On the stability of the quadratic mapping in normed spaces
Department of Mathematics, Kangnam University, Suwon 449-702, South Korea
Received 3 December 1999; Revised 28 February 2000
Copyright © 2001 Gwang Hui Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The Hyers-Ulam stability, the Hyers-Ulam-Rassias stability, and
also the stability in the spirit of Gavruţa for each of
the following quadratic functional equations f(x+y)+f(x−y)=2f(x)+2f(y), f(x+y+z)+f(x−y)+f(y−z)+f(z−x)=3f(x)+3f(y)+3f(z), f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(z+x) are investigated.