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2016 Generalizations of Majorization Inequality via Lidstone's Polynomial and Their Applications
M. Adil Khan, N. Latif, J. Pecaric
Commun. Math. Anal. 19(2): 101-122 (2016).

Abstract

In this paper, we obtain the generalizations of majorization inequalities by using Lidstone's interpolating polynomials and conditions on Green's functions. We give bounds for identities related to the generalizations of majorization inequalities by using Čebyšev functionals. We also give Grüss type inequalities and Ostrowski-type inequalities for these functionals. We present mean value theorems and $n$-exponential convexity which leads to exponential convexity and then log-convexity for these functionals. We give some families of functions which enable us to construct a large families of functions that are exponentially convex and also give Stolarsky type means with their monotonicity.

Citation

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M. Adil Khan. N. Latif. J. Pecaric. "Generalizations of Majorization Inequality via Lidstone's Polynomial and Their Applications." Commun. Math. Anal. 19 (2) 101 - 122, 2016.

Information

Published: 2016
First available in Project Euclid: 11 February 2017

zbMATH: 1357.26030
MathSciNet: MR3580453

Subjects:
Primary: 26D15, 26D20, 26D99

Rights: Copyright © 2016 Mathematical Research Publishers

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Vol.19 • No. 2 • 2016
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