Hardy type inequalities for superquadratic functions via Jackson Nörlund integrals

Volume 23, Issue 3, pp 203--212 http://dx.doi.org/10.22436/jmcs.023.03.04

Publication Date: November 01, 2020 Submission Date: March 31, 2020 Revision Date: April 17, 2020 Accteptance Date: August 17, 2020

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Authors

Hafiz Abdul Moeed - Department of Mathematics, University of Lahore, Sargodha Campus, Pakistan. Dawood Ahmad - Department of Mathematics, University of Lahore, Sargodha Campus, Pakistan. Ammara Nosheen - Department of Mathematics, University of Lahore, Sargodha Campus, Pakistan. Khuram Ali Khan - Department of Mathematics, University of Sargodha, Sargodha, Pakistan.

Abstract

In this paper, it is tried to describe Hardy-type inequalities with certain kernels by using Jackson Nörlund integrals. In order to obtain the desired Hardy type inequalities, firstly, we prove Jensen's inequality involving super quadratic function and Jackson Nörlund integrals. Further, we discuss Hardy-type inequalities by choosing special kernels. Polya-Knopp type inequalities are also deduced to find applications.

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Keywords

• Hahn integral operators
• superquadratic function
• Hardy-type inequalities

MSC

•  26D10
•  26D15
•  39B62
•  26A51

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