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2012 On Discrete Favard's and Berwald's Inequalities
N. Latif, I. Perić, J. Pečarić
Commun. Math. Anal. 12(2): 34-57 (2012).


In this paper, we obtain an extensions of majorization type results and extensions of weighted Favard's and Berwald's inequality. We prove positive semi-definiteness of matrices generated by differences deduced from majorization type results and differences deduced from weighted Favard's and Berwald's inequality. This implies a surprising property of exponentially convexity and $\log$-convexity of this differences which allows us to deduce Lyapunov's inequalities for the differences, which are improvements of majorization type results and weighted Favard's and Berwald's inequalities. Analogous Cauchy's type means, as equivalent forms of exponentially convexity and log-convexity, are also studied and the monotonicity properties are proved.


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N. Latif. I. Perić. J. Pečarić. "On Discrete Favard's and Berwald's Inequalities." Commun. Math. Anal. 12 (2) 34 - 57, 2012.


Published: 2012
First available in Project Euclid: 16 March 2012

zbMATH: 1263.26008
MathSciNet: MR2905130

Primary: 26A24
Secondary: 26A51‎ , 26D15

Keywords: ‎Cauchy means , convex function , Dresher's type of means , exponential convexity , ‎generalized Favard's inequality , Log-convexity , Lypunov's inequality , majorization , positive semi-definite matrix

Rights: Copyright © 2012 Mathematical Research Publishers

Vol.12 • No. 2 • 2012
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