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

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.
 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)