Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces

We obtain the general solution of the generalized mixed additive and quadratic functional equation fx+my+fx−my=2fx−2m2fy+m2f2y, m is even; fx+y+fx−y−2m2−1fy+m2−1f2y, m is odd, for a positive integer m. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spa...

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Main Authors:	Abasalt Bodaghi, Sang Og Kim
Format:	Article
Language:	English
Published:	Hindawi Limited 2013-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2013/198018

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spelling	doaj-db13e46db3f342f3b04c35edc891d2002020-11-24T22:48:05ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/198018198018Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed SpacesAbasalt Bodaghi0Sang Og Kim1Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, IranDepartment of Mathematics, Hallym University, Chuncheon 200-702, Republic of KoreaWe obtain the general solution of the generalized mixed additive and quadratic functional equation fx+my+fx−my=2fx−2m2fy+m2f2y, m is even; fx+y+fx−y−2m2−1fy+m2−1f2y, m is odd, for a positive integer m. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces when m is an even positive integer or m=3.http://dx.doi.org/10.1155/2013/198018
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Abasalt Bodaghi Sang Og Kim
spellingShingle	Abasalt Bodaghi Sang Og Kim Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces Abstract and Applied Analysis
author_facet	Abasalt Bodaghi Sang Og Kim
author_sort	Abasalt Bodaghi
title	Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces
title_short	Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces
title_full	Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces
title_fullStr	Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces
title_full_unstemmed	Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces
title_sort	stability of a functional equation deriving from quadratic and additive functions in non-archimedean normed spaces
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2013-01-01
description	We obtain the general solution of the generalized mixed additive and quadratic functional equation fx+my+fx−my=2fx−2m2fy+m2f2y, m is even; fx+y+fx−y−2m2−1fy+m2−1f2y, m is odd, for a positive integer m. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces when m is an even positive integer or m=3.
url	http://dx.doi.org/10.1155/2013/198018
work_keys_str_mv	AT abasaltbodaghi stabilityofafunctionalequationderivingfromquadraticandadditivefunctionsinnonarchimedeannormedspaces AT sangogkim stabilityofafunctionalequationderivingfromquadraticandadditivefunctionsinnonarchimedeannormedspaces
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Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces

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