A variant of Jensen–Steffensen's inequality and quasi-arithmetic means

By S. Abramovich, M. K. Bakula, M. Matic, Josip E. Pecaric. 2005

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A variant of Jensen-Steffensen's inequality is proved. Necessary and sufficient conditions for the equality in Jensen-Steffensen's inequality are established. Several inequalities involving more than two monotonic functions and generalized quasi-arithmetic means with not only positive weights are proved. It is shown that such generalized quasi-arithmetic means have the same comparability properties as those with positive weights.

Subfields: Applied Mathematics

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