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Properties of mappings related to the Minkowski inequality. (English) Zbl 1232.26033
Summary: We obtain properties of several mappings which are arisen from the Minkowski inequality. We investigate superadditivity (subadditivity) and monotonicity of those functions, and give some refinements of the Minkowski inequality and the Hölder inequality.
MSC:
26D15Inequalities for sums, series and integrals of real functions
28A25Integration with respect to measures and other set functions
References:
[1]Dragomir S.S., Pečarić J.E., Persson L.E.: Properties of some functionals related to Jensen’s inequality. Acta Math. Hungar 70(1–2), 129–143 (1996) · Zbl 0847.26013 · doi:10.1007/BF00113918
[2]E. H. Lieb and M. Loss, Analysis, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, 2001.
[3]McLaughlin H.W., Metcalf F.T.: The Minkowski and Tchebychef inequalities as functions of the index set. Duke Math. J. 35, 865–873 (1968) · Zbl 0183.05002 · doi:10.1215/S0012-7094-68-03594-1
[4]Pečarić J.E.: Improvements of H”older’s and Minkowski’s inequalities. Mat. Bilten 17, 69–74 (1993)
[5]J. E. Pečarić, F. Proschan and Y. L. Tong, Convex functions, partial orderings, and statistical applications, Academic Press Inc., 1992.
[6]Vasić P.M., Pečarić J.E.: On the Hölder and some related inequalities. Rev. Anal. Numér. Théor. Approx. 25(48), 95–103 (1982) No 1