Communications in Mathematical Analysis

On Discrete Favard's and Berwald's Inequalities

N. Latif, I. Perić, and J. Pečarić

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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.

Article information

Commun. Math. Anal., Volume 12, Number 2 (2012), 34-57.

First available in Project Euclid: 16 March 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A24
Secondary: 26A51 26D15: Inequalities for sums, series and integrals

Convex function majorization generalized Favard's inequality positive semi-definite matrix exponential convexity log-convexity Lypunov's inequality Dresher's type of means Cauchy means


Latif, N.; Pečarić, J.; Perić, I. On Discrete Favard's and Berwald's Inequalities. Commun. Math. Anal. 12 (2012), no. 2, 34--57.

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