STABILITY OF AN <i>l</i>-VARIABLE CUBIC FUNCTIONAL

Abstract

Using the direct and fixed point methods, we obtain the solution and prove the Hyers-Ulam stability of the l-variable cubic functional equation f(Sigma(l)(i=1) x(i)) + Sigma(l)(j=1) f (-lx(j) + Sigma(l)(i=1i not equal j) x(i)) = - 2(l + 1) Sigma(i=1),(l)(i not equal j not equal k) f(x(i) + x(j) + x(k)) + (3l(2) - 2l - 5) Sigma(i=1),(l)(i not equal j) f(x(i) + x(j)) - 3(l(3) - l(2) - l + 1) Sigma(l)(i=1) f(x(i)), l is an element of N, l >= 3, in random normed spaces.