Further refinements of the Jensen inequalities based upon samples with repetitions. (English) Zbl 1190.26031
Summary: We give a new refinement and extension of the well-known Jensen inequality for any mid-convex function \(f\) by arithmetic means of \(f\) evaluated at weighted arithmetic means of samples with repetitions. Our refinement provides the perfected and corrected version of the results given earlier by J. E. Pečarić and D. Svrtan [J. Math. Anal. Appl. 222, 365–373 (1998; Zbl 0912.26008)]. As generalizations, we also obtain two other refinements of Jensen’s inequality.
Keywords:
Jensen’s inequality; refinements and extensions; mid-convex function; arithmetic means; weighted arithmetic means; samples with repetitionsCitations:
Zbl 0912.26008References:
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