Hyers-Ulam-Rassias stability of a finite variable cubic functional equation in matrix paranormed spaces

Abstract

We introduce the finite variable cubic functional equation of the form Sigma(m)(a=1)phi(-t(a)+(m)Sigma(b=1;a not equal b)t(b))-(m)Sigma(a-1)phi(2t(a))=(m-6)Sigma(1 <= a<b<c <= m)phi(t(a)+t(b)+t(c)) +(-m(2)+9m-14)Sigma(1 <= a<b <= m)phi(t(a)+t(b)) +(m(3)-11m(2)+28m-36/2)(m)Sigma(a=1)phi(t(a)) where m >= 4 is a fixed integer, and we establish the Hyers-Ulam-Rassias stability results in paranormed spaces and matrix paranormed spaces