Communications in Mathematical Analysis
- Commun. Math. Anal.
- Volume 19, Number 2 (2016), 101-122.
Generalizations of Majorization Inequality via Lidstone's Polynomial and Their Applications
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.
Commun. Math. Anal., Volume 19, Number 2 (2016), 101-122.
First available in Project Euclid: 11 February 2017
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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
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