Naslov
On discrete Favard's and Berwald's inequalities

Autori
Latif, N. ; Pečarić, J. ; Perić, I.

Izvornik
Communications in mathematical analysis (1938-9787) 12 (2012), 2; 34-57

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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