%0 Journal Article
%T On the stability of the Pexiderized cubic functional equation in multi-normed spaces
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Nazarianpoor, Mahdi
%A Sadeghi, Ghadir
%D 2018
%\ 01/01/2018
%V 09
%N 1
%P 45-83
%! On the stability of the Pexiderized cubic functional equation in multi-normed spaces
%K Hyers-Ulam stability
%K Multi-normed space
%K Cubic functional equation
%K Pexiderized cubic functional equation
%K $2$-variables cubic functional equation
%R 10.22130/scma.2018.24755
%X 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.
%U https://scma.maragheh.ac.ir/article_24755_41cdb890766a677f5346e922caa5ad31.pdf