Stability of a Quartic Functional Equation

We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x − my) = 2(7m − 9)(m − 1)f(x) + 2m (2)(m (2) − 1)f(y)−(m − 1)(2) f(2x) + m (2){f(x + y) + f(x − y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by t...

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Detalles Bibliográficos
Autor principal: Bodaghi, Abasalt
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3922033/
https://www.ncbi.nlm.nih.gov/pubmed/24587750
http://dx.doi.org/10.1155/2014/752146
Descripción
Sumario:We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x − my) = 2(7m − 9)(m − 1)f(x) + 2m (2)(m (2) − 1)f(y)−(m − 1)(2) f(2x) + m (2){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.

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