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A variant of Jensen-Steffensen's inequality and quasi-arithmetic means |
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| Authors: | S. Abramovich J. Pe?ari? |
| Affiliation: | a Department of Mathematics, University of Haifa, Haifa, 31905, Israel b Department of Mathematics, Faculty of Natural Sciences, Mathematics and Education, University of Split, Teslina 12, 21000 Split, Croatia c Faculty of textile technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia |
| Abstract: | 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. |
| Keywords: | Jensen-Steffensen's inequality Monotonicity Quasi-arithmetic means Power means |
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