Generalized Stability of Euler-Lagrange Quadratic Functional Equation

The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equation f(ax+by)+af(x-by)=(a+1)b2f(y)+a(a+1)f(x), in (β,p)-Banach space, where a,b are fixed rational numbers such that...

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Main Authors: Hark-Mahn Kim, Min-Young Kim
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/219435
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author Hark-Mahn Kim
Min-Young Kim
author_facet Hark-Mahn Kim
Min-Young Kim
author_sort Hark-Mahn Kim
collection DOAJ
description The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equation f(ax+by)+af(x-by)=(a+1)b2f(y)+a(a+1)f(x), in (β,p)-Banach space, where a,b are fixed rational numbers such that a≠-1,0 and b≠0.
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spelling doaj-art-cb4e91e6a6834978b80d81ef1d85b6d02025-02-03T01:03:15ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/219435219435Generalized Stability of Euler-Lagrange Quadratic Functional EquationHark-Mahn Kim0Min-Young Kim1Department of Mathematics, Chungnam National University, 79 Daehangno, Yuseong-gu, Daejeon 305-764, Republic of KoreaDepartment of Mathematics, Chungnam National University, 79 Daehangno, Yuseong-gu, Daejeon 305-764, Republic of KoreaThe main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equation f(ax+by)+af(x-by)=(a+1)b2f(y)+a(a+1)f(x), in (β,p)-Banach space, where a,b are fixed rational numbers such that a≠-1,0 and b≠0.http://dx.doi.org/10.1155/2012/219435
spellingShingle Hark-Mahn Kim
Min-Young Kim
Generalized Stability of Euler-Lagrange Quadratic Functional Equation
Abstract and Applied Analysis
title Generalized Stability of Euler-Lagrange Quadratic Functional Equation
title_full Generalized Stability of Euler-Lagrange Quadratic Functional Equation
title_fullStr Generalized Stability of Euler-Lagrange Quadratic Functional Equation
title_full_unstemmed Generalized Stability of Euler-Lagrange Quadratic Functional Equation
title_short Generalized Stability of Euler-Lagrange Quadratic Functional Equation
title_sort generalized stability of euler lagrange quadratic functional equation
url http://dx.doi.org/10.1155/2012/219435
work_keys_str_mv AT harkmahnkim generalizedstabilityofeulerlagrangequadraticfunctionalequation
AT minyoungkim generalizedstabilityofeulerlagrangequadraticfunctionalequation