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

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

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

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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 $\check{C}$eby$\check{s}$ev functionals. We also give Gr$\ddot{u}$ss 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.