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Generalized Cauchy difference equations. II. (English) Zbl 1206.39022
Author’s abstract: The main result is an improvement of previous results on the equation
$f(x)+f(y)-f(x+y)=g[\phi(x)+\phi(y)-\phi(x+y)]$
for a given function $$\phi$$. We find its general solution assuming only continuous differentiability and local nonlinearity of $$\phi$$. 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 $$f_0,g_0$$. Here we weaken the assumptions on $$f_0,g_0$$ considerably and find all solutions under slightly stronger regularity assumptions on $$H$$.
[For part I, see Aequationes Math. 70, No. 1–2, 154–176 (2005; Zbl 1079.39017).]

##### MSC:
 39B22 Functional equations for real functions
Full Text:
##### References:
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