On the Jensen-Steffensen inequality for generalized convex functions

M. Bakula; A. Matković; J. Pečarić

doi:10.1007/s10998-007-3019-x

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 55: Issue 1

On the Jensen-Steffensen inequality for generalized convex functions

Authors:

M. Bakula

M. Bakula University of Split Department of Mathematics, Faculty of Natural Sciences, Mathematics and Education Teslina 12 21000 Split Croatia

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A. Matković

A. Matković University of Split Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture Rudera Boškovića b.b. 21000 Split Croatia

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J. Pečarić

J. Pečarić University of Zagreb Faculty of Textile Technology Prilaz Baruna Filipovića 30 10000 Zagreb Croatia

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Pages:: 19–34

Online Publication Date:: 05 Sep 2007

Publication Date:: 01 Sep 2007

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s10998-007-3019-x

Keywords:: 26D15; 26B25; P -convex functions; functions with nondecreasing increments; Jensen-Steffensen inequality; Čebyšev’s inequality; Hölder’s inequality; generalized quasiarithmetic means

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Abstract

Jensen-Steffensen type inequalities for P-convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of H�lder’s inequality with weights satisfying the conditions as in the Jensen-Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)