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Jensen’s functional equation on groups. (English) Zbl 0688.39007
Let f be a map from a group G into an abelian group H satisfying the equation \(f(xy)+f(xy^{-1})=2f(x)\) for all \(x,y\in G\) with the normalisation condition \(f(e)=0\) where e denotes the identity of G and 0 that of H. Let S(G,H) denote the set of all solutions of the functional equation under reference. The author provides a description of S(G,H) for special groups G, including the free group on 2 generators, \(GL_ 2(Z)\) and the multiplicative group of some fields.
Reviewer: H.K.L.Vasudeva

39B52 Functional equations for functions with more general domains and/or ranges
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