Generalized results of majorization inequality via Lidstone's polynomial and newly Green functions

Volume 11, Issue 6, pp 812--831 http://dx.doi.org/10.22436/jnsa.011.06.08

Publication Date: May 03, 2018 Submission Date: January 02, 2017 Revision Date: January 02, 2018 Accteptance Date: March 08, 2018

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Authors

Nouman Siddique - Department of Mathematics, Govt. College University, Faisalabad 38000, Pakistan. Naveed Latif - General Studies Department, Jubail Industrial College, Jubail Industrial City 31961, Kingdom of Saudi Arabia. Josip Pečarić - Faculty of Textile Technology Zagreb, University of Zagreb, Prilaz Baruna Filipovica 28A, 10000 Zagreb, Croatia. - RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russia.

Abstract

Generalized results of majorization inequality are obtained by using newly Green functions defined in [N. Mahmood, R. P. Agarwal, S. I. Butt, J. Pečarić, J. Inequal. Appl., \({\bf2017}\) (2017), 17 pages] and Lidstone's polynomial. We find new upper bounds of Grüss and Ostrowski type. We give further results of majorization inequality by making linear functionals constructed on convex functions \(\frac{f(x)}{x}\). Some applications are given.

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Keywords

• Classical majorization theorem
• Fuchs's thorem
• Lidstone's interpolating polynomial
• Green Function for 'two point right focal' problem
• Čebyšev functional
• Grüss type upper bounds
• Ostrowski-type bounds
• convex function \(f(x)/x\)
• n-exponentially convex function
• mean value theorems
• Stolarsky type means

MSC

•  26D07
•  26D15
•  26D20
•  26D99

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