On the Fuzzy Stability of an Affine Functional Equation

TL;DR

This paper finds the general solution to a specific affine functional equation and proves its stability in fuzzy normed spaces, extending classical stability results to fuzzy contexts.

Contribution

It provides the first stability analysis of this functional equation within fuzzy normed spaces, including the general solution and stability conditions.

Findings

General solution of the functional equation derived

Established Hyers-Ulam-Rassias stability in fuzzy normed spaces

Confirmed stability in the sense of Hyers and Ulam for the equation

Abstract

In this paper, we obtain the general solution of the following functional equation f(3x + y + z) + f(x + 3y + z) + f(x + y + 3z) + f(x) + f(y) + f(z) = 6f(x + y + z): We establish the Hyers-Ulam-Rassias stability of the above functional equation in the fuzzy normed spaces. Further we show the above functional equation is stable in the sense of Hyers and Ulam in fuzzy normed spaces.