@article {
author = {Nazarianpoor, Mahdi and Sadeghi, Ghadir},
title = {On the stability of the Pexiderized cubic functional equation in multi-normed spaces},
journal = {Sahand Communications in Mathematical Analysis},
volume = {09},
number = {1},
pages = {45-83},
year = {2018},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2018.24755},
abstract = {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.},
keywords = {Hyers-Ulam stability,Multi-normed space,Cubic functional equation,Pexiderized cubic functional equation,$2$-variables cubic functional equation},
url = {https://scma.maragheh.ac.ir/article_24755.html},
eprint = {https://scma.maragheh.ac.ir/article_24755_41cdb890766a677f5346e922caa5ad31.pdf}
}