title: Stability of a quartic functional equation.
abstract: 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.
authors.affiliation: Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran.
authors.forename: Abasalt
authors.identifier: 0000-0003-0358-4518
authors.initials: A
authors.lastname: Bodaghi
mesh_terms: D000465:Algorithms; D055641:Mathematical Concepts; D008962:Models, Theoretical