The Cauchy functional equations in distributions

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The Pompeiu functional equation is defined by Neagu for Schwartz distributions. His method is extended to the four Cauchy functional equations by means of two new operators Q ∗ {Q^*} and R ∗ {R^*} on D ′ ( I ) \mathcal {D}’(I) . The Cauchy equations in distributions reduce to the classical equations when the solutions are regular distributions, i.e. locally integrable functions.