International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 11, Pages 721-727
doi:10.1155/S0161171200005184

Stability of generalized additive Cauchy equations

Soon-Mo Jung1 and Ki-Suk Lee2

1Mathematics Section, College of Science and Technology, Hong-Ik University, Chochiwon 339-701, Korea
2Department of Mathematics Education, Korea National University of Education, Choongbook, Chongwon 363-791, Korea

Received 9 May 2000

Copyright © 2000 Soon-Mo Jung and Ki-Suk Lee. 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

A familiar functional equation f(ax+b)=cf(x) will be solved in the class of functions f:ℝ→ℝ. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f(a1x1+⋯+amxm+x0)=∑i=1mbif(ai1x1+⋯+aimxm) in connection with the question of Rassias and Tabor.