engleski

Superadditivity of some Jensen-type functionals

In 1996. S. S. Dragomir, J. Pečarić and L. E. Persson investigated discrete Jensen’s functional. They proved that, under the assumption of convexity of the involved function, this functional is superadditive and increasing on the set of all nonnegative weighted n-tuples. Motivated by their results, we prove the analogues ones for Jessen’s functional, as well as for McShane’s functional, which is a multidimensional generalization of Jessen’s functional. Consequently, we establish their lower and upper bounds expressed by the non weighted functionals of the same type. Such bounds enable us to obtain converses and refinements of the series of the classical inequalities, such are arithmetic-geometric inequality, Young’s and H¨older’s inequality in the difference and quotient form, as well as some other related inequalities.

superadditivity; Jensen inequality; functional; monotonicity; bounds

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