×

Non-Archimedean stability of partitioned functional equations. (English) Zbl 1291.39052

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.

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
PDFBibTeX XMLCite
Full Text: Link