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In 1940, Ulam [1] gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. Among these was the following question concerning the stability of homomorphisms. We are given a group G and a metric group G′ with metric ρ(·,·). Given > 0, does there exist a δ > 0 such that if f :G→G′ satisfies ρ((More)
In this article, we prove the generalized Hyers–Ulam stability of the following Cauchy additive functional equation f x − y n + z + f y − z n + x + f z − x n + y = f (x + y + z) in fuzzy Banach spaces for any fixed nonzero integer n. A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull.