Stability of Functional Inequalities with Cauchy-Jensen Additive Mappings
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چکیده
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( f (xy), f (x) f (y)) < δ for all x, y ∈G, then a homomorphism h :G→G′ exists with ρ( f (x),h(x)) < for all x ∈G? In 1941, Hyers [2] considered the case of approximately additive mappings f : E→ E′, where E and E′ are Banach spaces and f satisfies Hyers’ inequality
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تاریخ انتشار 2007