×

An AQCQ-functional equation in normed 2-Banach spaces. (English) Zbl 1325.39023

The concept of stability for a functional equation arises when one replaces a functional equation by inequality, which acts as a perturbation of the equation. In the \(1940\) S. M. Ulam posed the first stability problem. In the following year, D. H. Hyers [Proc. Natl. Acad. Sci. USA 27, 222–224 (1941; Zbl 0061.26403)] gave a partial affirmative answer to the question of Ulam. Hyers’ theorem was generalized by T. Aoki [J. Math. Soc. Japan 2, 64–66 (1950; Zbl 0040.35501)] for additive mappings and by T. M. Rassias [Proc. Am. Math. Soc. 72, 297–300 (1978; Zbl 0398.47040)] for linear mappings by considering an unbounded Cauchy difference. In the present work, the authors prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic (AQCQ) functional equation in \(2\)-Banach spaces.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
39B55 Orthogonal additivity and other conditional functional equations
PDFBibTeX XMLCite