On some equations stemming from quadrature rules
Abstract
We deal with functional equations of the type F(y) − F(x) = (y − x) Σₖ fₖ((1 − λₖ)x + λₖy), connected to quadrature rules and, in particular, we find the solutions of the following functional equation f(x) − f(y) = (x − y)[g(x) + h(x + 2y) + h(2x + y) + g(y)]. We also present a solution of the Stamate type equation yf(x) − xf(y) = (x − y)[g(x) + h(x + 2y) + h(2x + y) + g(y)]. All results are valid for functions acting on integral domains.
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