The applications of functional variants of Jensen's inequality (Q2443690)

In [Mat. Tidsskr. B 2, 17--28 (1931; Zbl 0002.38804)], \textit{B. Jessen} formulated the functional form of the classical Jensen inequality for convex functions of one variable. In [Bull. Am. Math. Soc. 43, 521--527 (1937; Zbl 0017.16003; JFM 63.0160.01)], \textit{E. J. McShane} extended this functional form to convex functions of several variables. In the paper under review, the author offers applications and generalizations of McShane's results. By using the positive linear functionals, generalizations of Jensen's inequality are deduced.