On the Cauchy difference on normed spaces |
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Authors: | J Brzdçk |
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Institution: | 1. Department of Mathematics, Pedagogical University, Rejtana 16 A, 35-310 Rzeszów, Poland
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Abstract: | LetX be a real linear normed space, (G, +) be a topological group, andK be a discrete normal subgroup ofG. We prove that if a continuous at a point or measurable (in the sense specified later) functionf:X →G fulfils the condition:f(x +y) -f(x) -f(y) ∈K whenever ‖x‖ = ‖y‖, then, under some additional assumptions onG,K, andX, there esists a continuous additive functionA :X →G such thatf(x) -A(x) ∈K. |
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