Rad HAZU, Matematičke znanosti, Vol. 19 (2015), 91-116.
GENERALIZATION OF MAJORIZATION THEOREM VIA ABEL-GONTSCHAROFF POLYNOMIAL
Muhammad Adil Khan, Naveed Latif and Josip Pečarić
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
e-mail: adilswati@gmail.com
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.
Full text (PDF) (free access)
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