International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 475-478
doi:10.1155/S0161171298000672
On a modified Hyers-Ulam stability of homogeneous equation
Mathematical Part, College of Science & Technology, Hong-Ik University, Chochiwon 339-800, South Korea
Received 21 February 1996
Copyright © 1998 Soon-Mo Jung. 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
In this paper, a generalized Hyers-Ulam stability of the homogeneous equation shall be
proved, i.e., if a mapping f satisfies the functional inequality ‖f(yx)−ykf(x)‖≤φ(x,y) under suitable
conditions, there exists a unique mapping T
satisfying T(yx)=ytT(x)
and ‖T(x)−f(x)‖≤Φ(x).