We show that the functional equation g(x + y/2) = 4√g(x)g(y) is stable in the classical sense on arbitrary ℚ-algebraically open convex sets, but the Hyers method does not work. For the convenience of the reader, we have included an extensive list of references where stability theorems for functional equations were obtained using the direct method of Hyers.
|Number of pages||11|
|Journal||Journal of Inequalities in Pure and Applied Mathematics|
|Publication status||Published - Apr 15 2005|
- Cauchy's functional equation
- Hyers iteration
ASJC Scopus subject areas
- Applied Mathematics