The problem “If we replace a given functional equation by a functional inequality, when can one assert that the solutions of the inequality must be close to the solutions of the given equation?” is the essence of Hyers-Ulam-Rassias stability theory; cf. Th. M. Rassias [Acta Appl. Math. 62, No. 1, 23–130 (2000; Zbl 0981.39014)].
For a mapping between real vector spaces, let us define to be and .
In the paper under review, the author determines the general solution for the mixed type functional equation
and proves its Hyers-Ulam-Rassias stability by using the Hyers type sequences; see Th. M. Rassias [J. Math. Anal. Appl. 158, No. 1, 106–113 (1991; Zbl 0746.46038)].