Stability of a functional equation deriving from quadratic and additive functions in non-Archimedean normed spaces
Summary: We obtain the general solution of the generalized mixed additive and quadratic functional equation \(f(x+my)+f(x-my)=2f(x)-2m^2f(y)+m^2f(2y)\), \(m\) is even; \(f(x+y)+f(x-y)-2(m^2-1)f(y)+(m^2-1)f(2y)\), \(m\) is odd, for a positive integer \(m\). We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces when \(m\) is an even positive integer or \(m=3\).
scientific article; zbMATH DE number 6306518
scientific article