Abstract
We introduce an arithmetic functional equation f(x2+y2)=f(x2)+f(y2) and then investigate stability estimates of the functional equation by using the Brzdȩk fixed point theorem on a non-Archimedean fuzzy metric space and a non-Archimedean fuzzy normed space. To apply the Brzdȩk fixed point theorem, the proof uses the linear relationship between two variables, x and y.
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