Annals of Functional Analysis

On majorization‎, ‎Favard and Berwald inequalities

Ivan Perić, Naveed ‎Latif‎, and Josip ‎Pečarić

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Abstract

‎In this paper‎, ‎we obtain 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 these differences‎ ‎which allows us to deduce Lyapunov's and Dresher's inequalities for these‎ ‎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

Source
Ann. Funct. Anal. Volume 2, Number 1 (2011), 31-50.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399900260

Digital Object Identifier
doi:10.15352/afa/1399900260

Mathematical Reviews number (MathSciNet)
MR2811205

Zentralblatt MATH identifier
1223.26006

Subjects
Primary: 26A24
Secondary: 26A51‎ ‎26D15

Keywords
majorization‎ ‎generalized Favard's inequality ‎generalized Berwald's inequality exponentially convexity ‎Cauchy means

Citation

‎Latif‎, Naveed; ‎Pečarić, Josip; Perić, Ivan. On majorization‎, ‎Favard and Berwald inequalities. Ann. Funct. Anal. 2 (2011), no. 1, 31--50. doi:10.15352/afa/1399900260. https://projecteuclid.org/euclid.afa/1399900260


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