New refinements of the Jensen inequalities based on samples with repetitions
The paper contains refinements of the Jensen inequality for a mid-convex real function \(f\) defined on a convex subset of a real linear space. The new inequalities involve \(f\) evaluated at arithmetic means of samples with repetitions. The case of samples without repetitions was treated previously by \textit{J. E. Pečarić} and \textit{V. Volenec} [Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. 197, No. 8-10, 463-467 (1988; Zbl 0683.26008)].
scientific article; zbMATH DE number 1218607