Solution of the Ulam Stability Problem for Euler--Lagrange--Jensen $k$-Cubic Mappings

S. A. Mohiuddine, John Michael Rassias, Abdullah Alotaibi

The ``oldest cubic'' functional equation was introduced and solved by the second author of this paper (see: Glas. Mat. Ser. III 36(56) (2001), no. 1, 63-72) which is of the form: \[ f(x+2y)=3f(x+y)+f(x-y)-3f(x)+6f(y). \] For further research in various normed spaces, we are introducing new cubic functional equations, and establish fundamental formulas for the general solution of such functional equations and for the ``Ulam stability'' of pertinent cubic functional inequalities.