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 $ \Upsilon $ possessing convex absolute derivatives. We establish connections of our results with several renowned results in the literature and also give applications to special functions.
Citation: Jia-Bao Liu, Saad Ihsan Butt, Jamshed Nasir, Adnan Aslam, Asfand Fahad, Jarunee Soontharanon. Jensen-Mercer variant of Hermite-Hadamard type inequalities via Atangana-Baleanu fractional operator[J]. AIMS Mathematics, 2022, 7(2): 2123-2141. doi: 10.3934/math.2022121
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 $ \Upsilon $ possessing convex absolute derivatives. We establish connections of our results with several renowned results in the literature and also give applications to special functions.
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Jia-Bao Liu, Saad Ihsan Butt, Jamshed Nasir, Adnan Aslam, Asfand Fahad, Jarunee Soontharanon. Jensen-Mercer variant of Hermite-Hadamard type inequalities via Atangana-Baleanu fractional operator[J]. AIMS Mathematics, 2022, 7(2): 2123-2141. doi: 10.3934/math.2022121
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