Abstract
Let (S, +) be a (semi)group and let (R,+, ·) be an integral domain. We study the solutions of a Pexider type functional equation $$f(x+y) + g(x+y) = f(x) + f(y) + g(x)g(y)$$ for functions f and g mapping S into R. Our chief concern is to examine whether or not this functional equation is equivalent to the system of two Cauchy equations $$\left\{\begin{array}{@{}ll} f(x+y) = f(x) + f(y)\\ g(x+y) = g(x)g(y)\end{array}\right.$$ for every \({x,y \in S}\).
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