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It is well known that the concept of Hyers-Ulam-Rassias stability was originated by Th. M. Rassias (1978) and the concept of Ulam-Gavruta-Rassias stability was originated by J. M. Rassias (1982–1989) and by P. Găvruta  (1999). In this paper, we give results concerning these two stabilities

Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias Stabilities of an Additive Functional Equation in Several Variables