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International Journal of Mathematics and Mathematical Sciences
Volume 21, Issue 3, Pages 475-478

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 Hindawi Publishing Corporation. 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.


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).