### GENERALIZATION OF MAJORIZATION THEOREM VIA ABEL-GONTSCHAROFF POLYNOMIAL

Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

Department of Mathematics, Govt. College University, Faisalabad 38000, Pakistan
e-mail: naveed707@gmail.com

Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb, Croatia
e-mail: pecaric@element.hr

Abstract.   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.

2010 Mathematics Subject Classification.   26D15, 26D20.

Key words and phrases.   Majorization inequality, Abel-Gontscharoff formula, Čebyšev functional, Ostrowski-type inequality, n-exponential convexity.

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