On the Hyers-Ulam stability of a generalized quadratic and additive functional equation

Kil-Woung Jun; Hark-Mahn Kim

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Bull. Korean Math. Soc. 2005; 42(1): 133-148

Printed March 1, 2005

On the Hyers-Ulam stability of a generalized quadratic and additive functional equation

Kil-Woung Jun and Hark-Mahn Kim

Chungnam National University, Chungnam National University

Abstract

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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