Stability of an Euler–Lagrange type Cubic Functional Equation

In this paper, we will find out the general solution and investigate the generalized Hyers–Ulam–Rassias stability problem for an Euler–Lagrange type cubic functional equation2mf(x + my) + 2f(mx − y) = (m^3 + m)[f(x+ y) + f(x − y)] + 2(m^4 − 1)f(y)in Banach spaces and in left Banach modules over a unital Banach ∗-algebra for a fixed integer m withm≠ 0,±1.