Stability of generalized Cauchy equations
2015
We investigate the stability of the functional equation
$$f(xy) = g(x)h(y) + k(y)$$
on amenable semigroups. This equation is a common generalization of two Pexider equations stemming from Cauchy’s additive and multiplicative functional equations, and it is a simple case of the Levi-Civita equation.
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