Communications in Mathematical Analysis

Generalizations of Majorization Inequality via Lidstone's Polynomial and Their Applications

M. Adil Khan, N. Latif, and J. Pecaric

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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.

Article information

Source
Commun. Math. Anal., Volume 19, Number 2 (2016), 101-122.

Dates
First available in Project Euclid: 11 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.cma/1486782021

Mathematical Reviews number (MathSciNet)
MR3580453

Zentralblatt MATH identifier
1357.26030

Subjects
Primary: 26D15: Inequalities for sums, series and integrals 26D20: Other analytical inequalities 26D99: None of the above, but in this section

Keywords
Majorization inequailty Lidstone's polynomial Green's function (2n)-convex function Čebyšev functional Grüss type inequality Ostrowski-type inequality $n$-exponentially convex function mean value theorems Stolarsky type means

Citation

Khan, M. Adil; Latif, N.; Pecaric, J. Generalizations of Majorization Inequality via Lidstone's Polynomial and Their Applications. Commun. Math. Anal. 19 (2016), no. 2, 101--122. https://projecteuclid.org/euclid.cma/1486782021


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