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Generalization of the power means and their inequalities. (English) Zbl 0753.26009
The paper contains a generalization of the power means which includes a class of positive nonlinear functionals. For these new means the author obtains generalizations of the fundamental mean inequality, Hölder’s, Minkowski’s and related inequalities.

MSC:
26D15 Inequalities for sums, series and integrals
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[1] Beesack, P.R.; Pečarić, J.E., On Jessen’s inequality for convex functions, J. math. anal. appl., 110, 536-552, (1985) · Zbl 0591.26009
[2] Pečarić, J.E.; Beesack, P.R., On Jessen’s inequality for convex functions, II, J. math. anal. appl., 118, 125-144, (1986) · Zbl 0608.26010
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[4] You, Guang-Rong, On Hölder’s inequalities for convexity, J. math. anal. appl., 143, 448-458, (1989) · Zbl 0688.26010
[5] Mitrinović, D.S.; Pečarić, J.E., Generalizations of the Jensen inequality, Österreich. akad. wiss. math.-natur. kl. sitzungsber. II, 196, 21-26, (1987), Heft 1-3 · Zbl 0639.26009
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