Non-stabilities of mixed type Euler-Lagrange k-cubic-quartic functional equation in various normed spaces

In this paper, we introduce and examine the generalized Ulam-Hyers stability of fixed Euler-Lagrange  k-Cubic-Quartic functional Equationf(x+ky) + f(kx+y) + f(x-ky) + f(y-kx) = k2[2f(x+y) + f(x-y) + f(y-x)] + 2(k4-1) [f(x) + f(y)] +k2/4(k2-1) [f(2x) + f(2y)]where k is a real number with k ≠ 0, ±1 in various Banach spaces with the help of two different methods.

Keywords:

cubic functional equation , quartic functional equations , mixed type functional equations , Generalized Hyers-Ulam stability , Banach space , Quasi-Beta Banach space , Fuzzy Banach space