Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 12404, 23 pages

Generalized orthogonal stability of some functional equations

Justyna Sikorska

Institute of Mathematics, University of Silesian, Bankowa 14, Katowice 40-007, Poland

Received 19 November 2005; Accepted 2 July 2006

Copyright © 2006 Justyna Sikorska. 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.


We deal with a conditional functional inequality xyf(x+y)f(x)f(y)ε(xp+yp), where is a given orthogonality relation, ε is a given nonnegative number, and p is a given real number. Under suitable assumptions, we prove that any solution f of the above inequality has to be uniformly close to an orthogonally additive mapping g, that is, satisfying the condition xyg(x+y)=g(x)+g(y). In the sequel, we deal with some other functional inequalities and we also present some applications and generalizations of the first result.