Ulam Stability of a Functional Equation in Various Normed Spaces

Abstract

In this note, we study the Ulam stability of a general functional equation in four variables. Since its particular case is a known equation characterizing the so-called bi-quadratic mappings (i.e., mappings which are quadratic in each of their both arguments), we get in consequence its stability, too. We deal with the stability of the considered functional equations not only in classical Banach spaces, but also in 2-Banach and complete non-Archimedean normed spaces. To obtain our outcomes, the direct method is applied.

Keywords

• Ulam stability
• functional equation
• bi-quadratic mapping
• 2-norm
• non-Archimedean norm