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Original scientific paper

Generalization of majorization theorem via Abel-Gontscharoff polynomial

Muhammad Adil Khan ; Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Naveed Latif ; Department of Mathematics, Govt. College University, Faisalabad 38000, Pakistan
Josip Pečarić ; Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb, Croatia

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page 91-116

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In this paper we use Abel-Gontscharoff formula and Green function to give some identities for the difference of majorization inequality and present the generalization of majorization theorem for the class of n-convex. We use inequalities for the Čebyšev functional to obtain bounds for the identities related to generalizations of majorization inequalities. We present mean value theorems and n-exponential convexity for the functional obtained from the generalized majorization inequalities. At the end we discuss the results for particular families of functions and give means.


Majorization inequality, Abel-Gontscharoff formula, Čebyšev functional, Ostrowski-type inequality, n-exponential convexity

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