Error bounds associated with different versions of Hadamard inequalities of mid-point type

Volume 23, Issue 3, pp 213--229 http://dx.doi.org/10.22436/jmcs.023.03.05

Publication Date: November 01, 2020 Submission Date: April 02, 2020 Revision Date: May 25, 2020 Accteptance Date: June 22, 2020

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Authors

Muhammad Raees - School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan. Matloob Anwar - School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan. Ghulam Farid - Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan.

Abstract

In this paper, we establish the error bounds of different versions of mid-point type inequalities. At first, we prove two identities for fractional integrals involving the extended generalized Mittag-Leffler function and generalized exponential fractional integrals, and then we establish the corresponding error bound inequalities. Furthermore, we find a generalized inequality for error bound inequalities using a generalized identity. Also, we find some inequalities which formulate all error bound inequalities for various versions of Hadamard inequality. Finally, we present some examples of the central moment of a random variable.

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Keywords

• Convex function
• extended generalized Mittag-Leffler function
• generalized integral
• Hadamard inequality

MSC

•  26D07
•  26D10
•  26D15
•  26A33

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