engleski

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

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.

Jensen-Steffensen's inequality; monotonicity; quasi-arithmetic means; power means

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