On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces

We establish the general solution of the functional equationf(nx+y)+f(nx-y)=[superscript]n2[/superscript] f(x+y)+[superscript]n2[/superscript] f(x-y)+2(f(nx)-[superscript]n2[/superscript] f(x))-2([superscript]n2[/superscript] -1)f(y) for fixed integers n with n≠0,±1 and investigate the generalized H...

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Published inJournal of inequalities and applications Vol. 2009; no. 1; p. 153084
Main Authors Gordji, M Eshaghi, Abbaszadeh, S, Park, Choonkil
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.01.2009
BioMed Central Ltd
SpringerOpen
Subjects
Banach spaces
Mathematical functions
Mathematical models
Mathematics
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Summary:We establish the general solution of the functional equationf(nx+y)+f(nx-y)=[superscript]n2[/superscript] f(x+y)+[superscript]n2[/superscript] f(x-y)+2(f(nx)-[superscript]n2[/superscript] f(x))-2([superscript]n2[/superscript] -1)f(y) for fixed integers n with n≠0,±1 and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.
ISSN:1025-5834
1029-242X
1029-242X
DOI:10.1186/1029-242X-2009-153084