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On the stability of the Pexiderized cubic functional equation in multi-normed spaces

Journal: Sahand Communications in Mathematical Analysis (Vol.9, No. 1)

Publication Date:

Authors : ; ;

Page : 45-83

Keywords : Hyers-Ulam stability; Multi-normed space; Cubic functional equation; Pexiderized cubic functional equation; $2$-variables cubic functional equation;

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In this paper, we investigate the Hyers-Ulam stability of the orthogonally  cubic equation and  Pexiderized cubic equation [f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),]in multi-normed spaces by the direct method and the fixed point method. Moreover, we prove the Hyers-Ulam stability of the  $2$-variables cubic  equation [ f(2x+y,2z+t)+f(2x-y,2z-t) =2f(x+y,z+t) +2f(x-y,z-t)+12f(x,z),]and orthogonally cubic type and $k$-cubic equation in multi-normed spaces. A counter example for non stability of the cubic equation is also discussed.

Last modified: 2018-02-03 20:15:59