Stability Estimates for an Arithmetic Functional Equation with Brzdȩk Fixed Point Approaches.

We introduce an arithmetic functional equation f (x 2 + y 2) = f (x 2) + f (y 2) 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. [ABSTRACT FROM AUTHOR]