Abstract
In this paper, some special mappings of several variables such as the multicubic and the multimixed quadratic–cubic mappings are introduced. Then, the systems of equations defining a multicubic and a multimixed quadratic–cubic mapping are unified to a single equation. Under some mild conditions, it is shown that a multimixed quadratic–cubic mapping can be multiquadratic, multicubic and multiquadratic–cubic. Furthermore, by applying a known fixed-point theorem, the Hyers–Ulam stability of multimixed quadratic–cubic, multiquadratic, multicubic and multiquadratic–cubic are studied in non-Archimedean normed spaces.
Highlights
The stability problems of functional equations are some of the classical and practical issues in the area of mathematical analysis, physics and engineering
A functional equation F is said to be stable if any mapping φ fulfilling F approximately is near to an exact solution of F
We describe the system of n equations defining a multimixed quadratic–cubic mapping as a single equation
Summary
The stability problems of functional equations are some of the classical and practical issues in the area of mathematical analysis, physics and engineering. Rassias was the first author who defined the cubic functional equation in [37] as follows: C(x + 2y) = 3C(x + y) + C(x – y) – 3C(x) + 6C(y). We prove the Hyers–Ulam stability and hyperstability of the multimixed quadratic–cubic mappings in non-Archimedean normed spaces by applying a known fixed-point theorem that was introduced and studied in [14]; for more applications of this method we refer to [4, 43] and [44].
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