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Research Article | Open Access

Jensen-Mercer variant of Hermite-Hadamard type inequalities via Atangana-Baleanu fractional operator

Jia-Bao Liu1Saad Ihsan Butt2( )Jamshed Nasir3Adnan Aslam4Asfand Fahad5Jarunee Soontharanon6( )
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
COMSATS University Islamabad, Lahore Campus, Pakistan
Virtual University Lahore Campus, Pakistan
University of Engineering and Technology, Lahore (RCET), Pakistan
COMSATS University Islamabad, Vehari Campus Campus, Pakistan
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand
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Abstract

We present new Mercer variants of Hermite-Hadamard (HH) type inequalities via Atangana-Baleanu (AB) fractional integral operators pertaining non-local and non-singular kernels. We establish trapezoidal type identities for fractional operator involving non-singular kernel and give Jensen-Mercer (JM) variants of Hermite-Hadamard type inequalities for differentiable mapping Υ possessing convex absolute derivatives. We establish connections of our results with several renowned results in the literature and also give applications to special functions.

CLC number: 26A51, 26D10, 26D15

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AIMS Mathematics
Pages 2123-2141

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Cite this article:
Liu J-B, Butt SI, Nasir J, et al. Jensen-Mercer variant of Hermite-Hadamard type inequalities via Atangana-Baleanu fractional operator. AIMS Mathematics, 2022, 7(2): 2123-2141. https://doi.org/10.3934/math.2022121

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Received: 27 April 2021
Accepted: 11 October 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)