University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101On the stability of the Pexiderized cubic functional equation in multi-normed spaces45832475510.22130/scma.2018.24755ENMahdi NazarianpoorDepartment of Mathematics and Computer
Sciences, Hakim Sabzevari University, Sabzevar, Iran.Ghadir SadeghiDepartment of Mathematics and Computer
Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.Journal Article20161022In this paper, we investigate the Hyers-Ulam stability of the orthogonally cubic equation and Pexiderized cubic equation <br />[<br />f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),<br />]<br />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 <br />[<br /> f(2x+y,2z+t)+f(2x-y,2z-t) =2f(x+y,z+t) +2f(x-y,z-t)+12f(x,z),<br />]<br />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.http://scma.maragheh.ac.ir/article_24755_41cdb890766a677f5346e922caa5ad31.pdf