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The generalized Hyers-Ulam stability of additive functional inequalities in non-Archimedean \(2\)-normed space. (English) Zbl 1474.39071

Summary: In this paper, we investigate the solution of the following functional inequality \[\|f(x)+f(y)+f(az), w\|\le \|f(x+y)-f(-az), w\|\] for some fixed non-zero integer \(a\), and prove the generalized Hyers-Ulam stability of it in non-Archimedean \(2\)-normed spaces.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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