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

Soon-Mo Jung

 Mathematical Part, College of Science & Technology, Hong-Ik University, Chochiwon 339-800, South Korea
Received 21 February 1996

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).