Generalized Cauchy Difference Equations. Ii
نویسنده
چکیده
The main result is an improvement of previous results on the equation f(x) + f(y)− f(x+ y) = g[φ(x) + φ(y)− φ(x+ y)] for a given function φ. We find its general solution assuming only continuous differentiability and local nonlinearity of φ. We also provide new results about the more general equation f(x) + f(y)− f(x+ y) = g(H(x, y)) for a given function H. Previous uniqueness results required strong regularity assumptions on a particular solution f0, g0. Here we weaken the assumptions on f0, g0 considerably and find all solutions under slightly stronger regularity assumptions on H.
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