An example of a stable functional equation when the Hyers method does not work

Zoltán Kaiser, Zsolt Páles

Research output: Contribution to journalArticle

5 Citations (Scopus)


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.

Original languageEnglish
Article number14
Pages (from-to)1-11
Number of pages11
JournalJournal of Inequalities in Pure and Applied Mathematics
Issue number1
Publication statusPublished - Apr 15 2005



  • Cauchy's functional equation
  • Hyers iteration
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this