Stability of a Quartic Functional Equation

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)+2m2(m2-1)f(y)-(m-1)2f(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 poi...

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Main Author: Abasalt Bodaghi
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2014/752146
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spelling doaj-c61387cda95d4fb7be73bf4732acd89f2020-11-25T01:37:49ZengHindawi LimitedThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/752146752146Stability of a Quartic Functional EquationAbasalt Bodaghi0Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, IranWe 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)2f(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.http://dx.doi.org/10.1155/2014/752146
collection DOAJ
language English
format Article
sources DOAJ
author Abasalt Bodaghi
spellingShingle Abasalt Bodaghi
Stability of a Quartic Functional Equation
The Scientific World Journal
author_facet Abasalt Bodaghi
author_sort Abasalt Bodaghi
title Stability of a Quartic Functional Equation
title_short Stability of a Quartic Functional Equation
title_full Stability of a Quartic Functional Equation
title_fullStr Stability of a Quartic Functional Equation
title_full_unstemmed Stability of a Quartic Functional Equation
title_sort stability of a quartic functional equation
publisher Hindawi Limited
series The Scientific World Journal
issn 2356-6140
1537-744X
publishDate 2014-01-01
description 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)2f(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.
url http://dx.doi.org/10.1155/2014/752146
work_keys_str_mv AT abasaltbodaghi stabilityofaquarticfunctionalequation
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