Sharikov, E. V. Hermite-Hadamard type inequalities for increasing radiant functions. (English) Zbl 1055.26021 JIPAM, J. Inequal. Pure Appl. Math. 4, No. 2, Paper No. 47, 13 p. (2003). The author calls “radiant function” a subhomogeneous one, i.e., satisfying \(f(ax)\leq af(x)\) for any \(a\in (0,1)\), and \(x\in\mathbb{R}^n_+\). Then, assuming also that if \(f> 0\) is increasing (i.e., \(x\geq y\) implies \(f(x)\geq f(y)\), where \(x\geq y\) means the coordinate-wise order relation), he proves Hadamard-type integral inequalities on \(\mathbb{R}^n_+\). We quote the following result in \(\mathbb{R}_+\): If \(f> 0\) is increasing and subhomogeneous on \([a,b]\), then \[ f(\sqrt{(b- a)^2+ b^2}- (b- a))\leq {1\over b-a} \int^b_a f(x)\,dx. \] Reviewer: József Sándor (Cluj-Napoca) Cited in 4 Documents MSC: 26D15 Inequalities for sums, series and integrals 26A51 Convexity of real functions in one variable, generalizations 26B25 Convexity of real functions of several variables, generalizations Keywords:integral inequalities; convex functions; subhomogeneous functions; Hadamard type inequality PDF BibTeX XML Cite \textit{E. V. Sharikov}, JIPAM, J. Inequal. Pure Appl. Math. 4, No. 2, Paper No. 47, 13 p. (2003; Zbl 1055.26021) Full Text: EuDML OpenURL