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JENSEN TYPE INEQUALITIES FOR Q-CLASS FUNCTIONS

Part of: Equations and inequalities involving nonlinear operators Inequalities

Published online by Cambridge University Press:  17 October 2011

MOHAMMAD SAL MOSLEHIAN  and
MOHSEN KIAN
MOHAMMAD SAL MOSLEHIAN*
Affiliation:
Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran (email: moslehian@ferdowsi.um.ac.ir, moslehian@member.ams.org)
MOHSEN KIAN
Affiliation:
Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran (email: kian_tak@yahoo.com)
*
✉For correspondence; e-mail: moslehian@ferdowsi.um.ac.ir
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Abstract

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Some inequalities of Jensen type for Q-class functions are proved. More precisely, a refinement of the inequality f((1/P)∑ ni=1pixi)≤P∑ ni=1(f(xi)/pi) is given in which p1,…,pn are positive numbers, P=∑ ni=1pi and f is a Q-class function. The notion of the jointly Q-class function is introduced and some Jensen type inequalities for these functions are proved. Some Ostrowski and Hermite–Hadamard type inequalities related to Q-class functions are presented as well.

Keywords

Q-class functionJensen’s inequalityjointly Q-classOstrowski type inequalityconvex functionHermite–Hadamard type inequality

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals 47J99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 1 , February 2012 , pp. 128 - 142
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This research was supported by a grant from Ferdowsi University of Mashhad (No. MP90210MOS).

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