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International Journal of Mathematics and Mathematical Sciences
Volume 25, Issue 4, Pages 217-229
http://dx.doi.org/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 Hindawi Publishing Corporation. 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(xy)=2f(x)+2f(y), f(x+y+z)+f(xy)+f(yz)+f(zx)=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.