Refinements of the integral Jensen’s inequality generated by finite or infinite permutations. (English) Zbl 1504.26052
Summary: There are a lot of papers dealing with applications of the so-called cyclic refinement of the discrete Jensen’s inequality. A significant generalization of the cyclic refinement, based on combinatorial considerations, has recently been discovered by the author. In the present paper we give the integral versions of these results. On the one hand, a new method to refine the integral Jensen’s inequality is developed. On the other hand, the result contains some recent refinements of the integral Jensen’s inequality as elementary cases. Finally some applications to the Fejér inequality (especially the Hermite-Hadamard inequality), quasi-arithmetic means, and \(f\)-divergences are presented.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26B25 | Convexity of real functions of several variables, generalizations |
Keywords:
discrete and integral Jensen inequalities; refinements; Fejér inequality; quasi-arithmetic means; \(f\)-divergencesReferences:
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