On a modified Hyers-Ulam stability of homogeneous equation
Soon-Mo Jung1
Received21 Feb 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).