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ON A GLOBAL UPPER BOUND FOR JESSEN’S INEQUALITY

Part of: Inequalities

Published online by Cambridge University Press:  01 October 2008

B. GAVREA ,
J. JAKŠETIĆ  and
J. PEČARIĆ
B. GAVREA
Affiliation:
Technical University of Cluj-Napoca, Department of Mathematics, Romania (email: bogdan.gavrea@math.utcluj.ro)
J. JAKŠETIĆ*
Affiliation:
University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Croatia (email: julije@math.hr)
J. PEČARIĆ
Affiliation:
University Of Zagreb, Faculty Of Textile Technology, Zagreb, Croatia (email: pecaric@mahazu.hazu.hr)
*
✉For correspondence; e-mail: julije@math.hr
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Abstract

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In two recent papers a global upper bound is derived for Jensen’s inequality for weighted finite sums. In this paper we generalize this result on positive normalized functionals.

Keywords

Jensen’s inequalityconvex functionspositive functionals

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 2 , October 2008 , pp. 246 - 257
Copyright
Copyright © Australian Mathematical Society 2009

References

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[3]Lupaş, A., “Mean value theorems for positive linear transformations” (Romanian with English summary), Rev. Anal. Numer. Teoria Aprox. 3 (1974) 121–140.Google Scholar
[4]Matković, A. and Pečarić, J., “A variant of Jensen’s inequality for convex functions of several variables”, J. Math. Inequal. 1 (2007) 45–51.CrossRefGoogle Scholar
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[6]Simić, S., “On a global upper bound for Jensen’s inequality”, J. Math. Anal. Appl. 343 (2008) 414–419.CrossRefGoogle Scholar