Stability of a cubic functional equation in 2-normed spaces (Q2927982)

Th. M. Rassias introduced the cubic functional equation NEWLINE\[NEWLINEf(2x+y)-3f(x+y)+3f(x)-f(x-y)=6f(y),NEWLINE\]NEWLINE and \textit{K.-W. Jun} and \textit{H.-M. Kim} [J. Math. Anal. Appl. 274, No. 2, 867--878 (2002; Zbl 1021.39014)], introduced the following cubic functional equation NEWLINE\[NEWLINEf(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x).NEWLINE\]NEWLINE In the present paper, the authors investigate a linear combination of the two functional equations above and prove the generalized Hyers-Ulam stability NEWLINE\[NEWLINEf(2x+y)+f(2x-y)=2f(x+2y)-4f(x+y)+18f(x)-12f(y)NEWLINE\]NEWLINE in 2-normed spaces.