Generalized Hyers-Ulam stability of sextic functional equation in random normed spaces

摘要

By using the direct and fixed point methods, we establish the general solution and generalized Hyers-Ulam stability of the following sextic functional equation f(nx + y) + f(nx - y) + f(x + ny) + f(x - ny) = (n~4+ n~2)[f(x + y) + f(x - y)] + 2(n~6 - n~4 - n~2+ 1)[f(x) + f(y)] in random normed spaces. Also, we present an illustrative example with the Lukasiewicz t-norm that can be a suitable approximation using this sextic function.