and Applied Analysis 3 for all x1, . . . , x2n âˆˆ V if and only if the odd mapping f : V â†’ W is Cauchy additive, that is, f ( x y ) f x f ( y ) , 2.2 for all x, y âˆˆ V . Proof. Assume that f : V â†’ Wâ€¦ (More)

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, containing the stability problem of homomorphisms asâ€¦ (More)

In 1940, Ulam proposed the general Ulam stability problem see 1 . Let G1 be a group and let G2 be a metric group with the metric d Â·, Â· . Given Îµ > 0, does there exist a Î´ > 0 such that if a mappingâ€¦ (More)

In 1940, Ulam proposed the stability problem see 1 . Let G1 be a group, and let G2 be a metric group with the metric d Â·, Â· . Given Îµ > 0, does there exist a Î´ > 0 such that if a mapping h : G1 â†’ G2â€¦ (More)

In 1940, Ulam proposed the stability problem see 1 : Let G1 be a group and let G2 be a metric group with the metric d Â·, Â· . Given Îµ > 0, does there exist a Î´ > 0 such that if a mapping h : G1 â†’ G2â€¦ (More)