Kenary, H. Azadi; Rassias, Th. M. Non-Archimedean stability of partitioned functional equations. (English) Zbl 1291.39052 Appl. Comput. Math. 12, No. 1, 76-90 (2013). The authors prove the generalized Hyers-Ulam stability of the following functional equation \[ (4p)^nf \left(\frac{x_1+\dots+x_{(4p)^n}}{(4p)^n}\right) + 4p \sum_{i=1}^{(4p)^{n-1}} f\left(\frac{x_{4pi-4p+1}+\dots + x_{4pi}}{4p}\right) = 2 \sum_{i=1}^{(4p)^n} f\left(\frac{x_i+x_{i+1}+x_{i+2}}{3}\right), \] where \(p\) is a prime number in a non-Archimedean normed space, by using standard techniques. Reviewer: Maryam Amyari (Mashhad) MSC: 39B82 Stability, separation, extension, and related topics for functional equations 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis 39B52 Functional equations for functions with more general domains and/or ranges Keywords:Hyers-Ulam-Rassias stability; non-Archimedean normed spaces PDFBibTeX XMLCite \textit{H. A. Kenary} and \textit{Th. M. Rassias}, Appl. Comput. Math. 12, No. 1, 76--90 (2013; Zbl 1291.39052) Full Text: Link