Solution of the Ulam stability problem for Euler-Lagrange-Jensen k-cubic mappings

Abstract

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.