The stability of a mixed type functional inequality with the fixed point alternative
Commun. Korean Math. Soc. 2004 Vol. 19, No. 2, 253-266
Printed June 1, 2004
Kyoo-Hong Park, Yong-Soo Jung
Seowon University, Chungnam National University
Abstract : In this note, by using the fixed point alternative, we investigate the modified Hyers-Ulam-Rassias stability for the following mixed type functional inequality which is either cubic or quadratic: \begin{eqnarray*} &&\|8f(x-3y)+24f(x+y)+f(8y) \\ &\quad& \ -8[f(x+3y)+3f(x-y)+2f(2y)]\|\leq \varphi(x,y). \end{eqnarray*}
Keywords : stability, cubic function, quadratic function, fixed point alternative
MSC numbers : 39B72, 39B52
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