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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: [email protected])
J. JAKŠETIĆ*
Affiliation:
University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Croatia (email: [email protected])
J. PEČARIĆ
Affiliation:
University Of Zagreb, Faculty Of Textile Technology, Zagreb, Croatia (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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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

[1]Cheung, W.-S., Matković, A. and Pečarić, J., “A variant of Jessen’s inequality and generalized means”, J. Inequal. Pure Appl. Math. 7 (2006) Article 10.Google Scholar
[2]Fejér, L., “Über die Fourierreihen II”, Math. Naturwiss. Anz. Ungar. Akd. Wiss. 24 (1906) 369–390.Google Scholar
[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
[5]Pečarić, J. E., Proschan, F. and Tong, Y. C., Convex functions, partial orderings and statistical applications (Academic Press, New York, 1992).Google Scholar
[6]Simić, S., “On a global upper bound for Jensen’s inequality”, J. Math. Anal. Appl. 343 (2008) 414–419.CrossRefGoogle Scholar