TY - JOUR
ID - 24755
TI - On the stability of the Pexiderized cubic functional equation in multi-normed spaces
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Nazarianpoor, Mahdi
AU - Sadeghi, Ghadir
AD - Department of Mathematics and Computer
Sciences, Hakim Sabzevari University, Sabzevar, Iran.
AD - Department of Mathematics and Computer
Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
Y1 - 2018
PY - 2018
VL - 09
IS - 1
SP - 45
EP - 83
KW - Hyers-Ulam stability
KW - Multi-normed space
KW - Cubic functional equation
KW - Pexiderized cubic functional equation
KW - $2$-variables cubic functional equation
DO - 10.22130/scma.2018.24755
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_24755.html
L1 - https://scma.maragheh.ac.ir/article_24755_41cdb890766a677f5346e922caa5ad31.pdf
ER -