TY  - JOUR
ID  - Kominek2008
LB  - Kominek2008
AU  - Kominek, Zygfryd
TI  - Remarks on the stability of some quadratic functional equations
ST  - Remarks on the stability of some quadratic functional equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2008
VL  - 28
IS  - 4
SP  - 517
EP  - 527
DO  - http://dx.doi.org/10.7494/OpMath.2008.28.4.517
UR  - http://dx.doi.org/10.7494/OpMath.2008.28.4.517
AB  - 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 \(\varphi\).
KW  - quadratic functional equations
KW  - stability
SN  - 1232-9274
ER  -