The generalized Hyers–Ulam–Rassias stability of a cubic functional equation

APPROXIMATION OF CUBIC MAPPINGS WITH n-VARIABLES IN β-NORMED LEFT BANACH MODULE ON BANACH ALGEBRAS

“…In this case, we see the equivalence of (1.1) and (1.2) (see [13]). Therefore, every solution of functional equations (1.1) and (1.2) is a cubic function (See Theorem 2.2 of [13]). For other cubic functional equations see [5], [12], [17]- [21].…”

“…Jun and Kim [10] introduced the following functional equation for all x ∈ X, and C is symmetric for each fixed one variable and is additive for fixed two variables. It is easy to see that the function f (x) = cx 3 satisfies the functional equation (1.1), so it is natural to call (1.1) the cubic functional equation and every solution of the cubic functional equation (1.1) is said to be a cubic function.…”

“…, where C is a cubic mapping and A is an additive mapping (see [11] and [14]). Hence f satisfies (2.1) since f is cubic.…”

A fixed point approach to the stability of an AQCQ-functional equation in RN-spaces

“…The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [3,5,12,13,20,26,29,45,46,47,48,49,50,51]). In [28], Jun and Kim considered the following cubic functional equation…”

Fuzzy Stability of an Aqcq-Functional Equation in Matrix Fuzzy Normed Spaces

“…Czerwik [15] proved the Hyers-Ulam stability of the quadratic functional equation. In [33], Jun and Kim considered the following cubic functional equation…”