On the Hyers-Ulam stability of a generalized quadratic and additive functional equation
Bull. Korean Math. Soc. 2005 Vol. 42, No. 1, 133-148
Published online March 1, 2005
Kil-Woung Jun and Hark-Mahn Kim
Chungnam National University, Chungnam National University
Abstract : In this paper, we obtain the general solution of a generalized quadratic and additive type functional equation \begin{eqnarray}\nonumber f(x+ay)+a f(x-y)=f(x-ay)+a f(x+y) \end{eqnarray} for any integer $a$ with $a \neq -1,0,1$ in the class of functions between real vector spaces and investigate the generalized Hyers-Ulam stability problem for the equation.
Keywords : Hyers-Ulam stability, quadratic function
MSC numbers : 39A11, 39B72
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