Stability of a quartic functional equation

ScientificWorldJournal. 2014 Jan 23:2014:752146. doi: 10.1155/2014/752146. eCollection 2014.


We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x - my) = 2(7m - 9)(m - 1)f(x) + 2m²(m² - 1)f(y)-(m - 1)² f(2x) + m²{f(x + y) + f(x - y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces.

MeSH terms

  • Algorithms
  • Mathematical Concepts*
  • Models, Theoretical*