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

S. Abramovich; M. Klaričić Bakula; M. Matić; J. Pečarić

doi:10.1016/j.jmaa.2004.10.027

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

S. Abramovich, M. Klaričić Bakula, M. Matić, J. Pečarić

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	370-386
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	307
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2004.10.027
State	Published - 1 Jul 2005

Keywords

Jensen-Steffensen's inequality
Monotonicity
Power means
Quasi-arithmetic means

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2004.10.027

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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.",

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AU - Pečarić, J.

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N2 - 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.

AB - 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.

KW - Jensen-Steffensen's inequality

KW - Monotonicity

KW - Power means

KW - Quasi-arithmetic means

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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