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A variant of Jessen’s inequality of Mercer’s type for superquadratic functions. (English) Zbl 1163.26323

Summary: A variant of Jessen’s inequality for superquadratic functions is proved. This is a refinement of a variant of Jessen’s inequality of Mercer’s type for convex functions. The result is used to refine some comparison inequalities of Mercer’s type between functional power means and between functional quasi-arithmetic means.

MSC:

26D15 Inequalities for sums, series and integrals
39B62 Functional inequalities, including subadditivity, convexity, etc.
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