Nazarianpoor, M., Sadeghi, G. (2018). On the stability of the Pexiderized cubic functional equation in multi-normed spaces. Sahand Communications in Mathematical Analysis, 9(1), 45-83.

Mahdi Nazarianpoor; Ghadir Sadeghi. "On the stability of the Pexiderized cubic functional equation in multi-normed spaces". Sahand Communications in Mathematical Analysis, 9, 1, 2018, 45-83.

Nazarianpoor, M., Sadeghi, G. (2018). 'On the stability of the Pexiderized cubic functional equation in multi-normed spaces', Sahand Communications in Mathematical Analysis, 9(1), pp. 45-83.

Nazarianpoor, M., Sadeghi, G. On the stability of the Pexiderized cubic functional equation in multi-normed spaces. Sahand Communications in Mathematical Analysis, 2018; 9(1): 45-83.

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

^{1}Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.

^{2}Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.

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.

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