@Article{Kominek2008,
author = "Kominek, Zygfryd",
title = "Remarks on the stability of some quadratic functional equations",
journal = "Opuscula Math.",
year = "2008",
volume = "28",
number = "4",
pages = "517--527",
doi = "http://dx.doi.org/10.7494/OpMath.2008.28.4.517",
url = "http://dx.doi.org/10.7494/OpMath.2008.28.4.517",
abstract = "Stability problems concerning the functional equations of the form \[f(2x+y)=4f(x)+f(y)+f(x+y)-f(x-y),\tag{1}\] and \[f(2x+y)+f(2x-y)=8f(x)+2f(y)\tag{2}\] are investigated. We prove that if the norm of the difference between the LHS and the RHS of one of equations \((1)\) or \((2)\), calculated for a function \(g\) is say, dominated by a function \(\varphi\) in two variables having some standard properties then there exists a unique solution \(f\) of this equation and the norm of the difference between \(g\) and \(f\) is controlled by a function depending on \(\varphi\).",
keywords = "quadratic functional equations, stability",
issn = "1232-9274"
}