Rubinov, A. M.; Dutta, J. Hadamard type inequality for quasiconvex functions in higher dimensions. (English) Zbl 1010.26017 J. Math. Anal. Appl. 270, No. 1, 80-91 (2002). As was established in [S. S. Dragomir and C. E. M. Pearce, Bull. Aust. Math. Soc. 57, No. 3, 373-385 (1998; Zbl 0908.26015)] , for a quasiconvex function \(f\) defined on \([a,b]\) we have \[ f\left( \frac{a+b}{2}\right) \leq \frac{2}{b-a}\int_{a}^{b}f(x) dx. \] This Hadamard type inequality is extended here for quasiconvex functions in higher dimensions. Reviewer: Gheorghe Toader (Cluj-Napoca) Cited in 1 ReviewCited in 3 Documents MSC: 26D15 Inequalities for sums, series and integrals 26B25 Convexity of real functions of several variables, generalizations Keywords:quasiconvex functions; Hadamard inequality; supremal generators Citations:Zbl 0908.26015 PDFBibTeX XMLCite \textit{A. M. Rubinov} and \textit{J. Dutta}, J. Math. Anal. Appl. 270, No. 1, 80--91 (2002; Zbl 1010.26017) Full Text: DOI References: [1] Dragomir, S. S.; Pečarić, J. E.; Persson, L. E., Some inequalities of Hadamard type, Soochow J. Math., 21, 335-341 (1995) · Zbl 0834.26009 [2] Dragomir, S. S.; Pearce, C. E.M., Quasi-convex functions and Hadamard’s inequality, Bull. Austral. Math. Soc., 57, 377-385 (1998) · Zbl 0908.26015 [3] Rubinov, A. M., Abstract Convexity and Global Optimization (2000), Kluwer Academic: Kluwer Academic Dordrecht · Zbl 0963.49014 [4] Pearce, C. E.M.; Rubinov, A. M., \(P\)-functions, quasiconvex functions and Hadamard-type inequalities, J. Math. Anal. Appl., 240, 92-104 (1999) · Zbl 0939.26009 [5] Kutateladze, S. S.; Rubinov, A. M., Minkowski duality and its applications, Russian Math. Surveys, 27, 137-192 (1972) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.