Filomat 2021 Volume 35, Issue 8, Pages: 2693-2704
https://doi.org/10.2298/FIL2108693B
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On the stability of a quadratic functional equation over non-Archimedean spaces
Bettencourt Gastão (Universidade da Beira Interior, Centro de Matemática e Aplicações (CMA-UBI), Covilhã, Portugal), gastao@ubi.pt
Mendes Sérgio (ISCTE - Lisbon University Institute, Lisbon, Portugal + Centro de Matemática e Aplicações (CMA-UBI), Covilhã, Portugal), sergio.mendes@iscte-iul.pt
Let G be an abelian group and suppose that X is a non-Archimedean Banach
space. We study Hyers-Ulam-Rassias stability for the functional equation of
quadratic type f(x+y+z)+ f(x)+f(y)+f(z)=f(x+y)+f(y+z)+ f(z+x) where f : G → X is a map.
Keywords: Hyers-Ulam stability, Fréchet functional equation, length function