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
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.