Inequalities involving multivariate convex functions. II. (English) Zbl 0699.26009

Neuman, Edward

Proc. Am. Math. Soc. 109, No. 4, 965-974 (1990).

Continuing the work of the author and of J. E. Pečarić [J. Math. Anal. Appl. 137, No.2, 541-549 (1989; Zbl 0672.26010)], this paper gives some inequalities for multivariate convex functions. Among them: a refinement of Jensen’s inequality and an extension of Fejér’s inequality [see D. S. Mitrinović and I. B. Lacković, Aequationes Math. 28, 229-232 (1985; Zbl 0572.26004)]. They are obtained with the aid of generalized simplex splines.

Reviewer: Gh.Toader

MSC:

26D15	Inequalities for sums, series and integrals
26B25	Convexity of real functions of several variables, generalizations
41A15	Spline approximation
33C60	Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)

Keywords:

multivariate convex functions; Jensen’s inequality; Fejér’s inequality; generalized simplex splines

Citations:

Zbl 0672.26010; Zbl 0572.26004