On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions
General solution of a Jensen type functional equation (in \(n\) variables) is determined for mappings of one real linear space into another. The equation stems from \textit{T. Popoviciu}'s characterization of convex functions via a functional inequality [An. Şti. Univ. Al. I. Cuza Iaşi, N. Ser., Secţ. Ia 11B, 155--164 (1965; Zbl 0166.06303)]. Stability problems for the equation are also considered, following the ideas taken from the papers by \textit{Th. M. Rassias} [Proc. Am. Math. Soc. {72}, 297--300 (1978; Zbl 0398.47040)], \textit{Z. Gajda} [Int. J. Math. Math. Sci. 14, 431--434 (1991; Zbl 0739.39013)] and \textit{P. Găvruţă} [J. Math. Anal. Appl. 184, 431--436 (1994; Zbl 0818.46043)].
scientific article; zbMATH DE number 1846010
scientific article