EXPONENTIAL CONVEXITY OF THE FAVARD'S INEQUALITY AND RELATED RESULTS

Naveed Latif, Josip Pečarić, Ivan Perić

Abstract


A b s t r a c t: In this paper we prove positive semi-definiteness of matrices generated by differences deduced from unweighted and weighted Favard's inequality. This implies a surprising property of exponential convexity of this differences which allows us to deduce Gram's, Lyapunov's and Dresher's types of inequalities for this differences.


Keywords


Favard's inequality; weighted Favard's inequality; positive semi-definite matrix; exponential convexity; log-convexity

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References


G. H. Hardy, J. E. Littlewood, G. Pólya: Inequalities, Cambridge University Press, Cambridge, 1978.

D. S. Mitrinović: Analytic Inequalities, Springer-Verlag, Berlin, 1970.

S. Karlin, W. J. Studden: Tchebycheff Systems, with Applications in Analysis and Statistics, Interscience, New York, 1966.

Matloob Anwar, J. Jakšetić, J. Pečarić and Atiq ur Rehman: Exponential convexity, positive semi-definite matrices and fundamental inequalities, submitted for publication J. Math. Inequal. to appear.

Naveed Latif, J. Pečarić and I. Perić: Some new results related to Favards inequality, J. Inequal. Appl, volume 2009, Article ID 128486, 14 pages, doi: 10.115/2009/128486.

J. Pečarić, F. Proschan and Y. L. Tong: Convex functions, Partial Orderings and Statistical Applications, Academic Press, New York, 1992.

T. Popoviciu. Sur quelques inégalités enter les fonctions convexes (I–III). C. R. Inst. Sc. Roumaine 2, 449–454, 454–458, and 3, 396–402 (1939).




DOI: http://dx.doi.org/10.20903/csnmbs.masa.2009.30.1-2.19

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