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A FUNCTIONAL EQUATION WITH RESTRICTED ARGUMENT RELATED TO COSINE FUNCTION

摘要


Let G be an abelian group, C be the field of complex numbers, and 0 6≠α∈ G be a fixed element. In this paper, we determine the general solution f, g : G→C of the functional equation f(x-y+α)+g(x+y+α) = 2 f(x) f(y) for all x; y ∈ G

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