Jensen-Mercer variant of Hermite-Hadamard type inequalities via Atangana-Baleanu fractional operator
Jia‐Bao Liu, Saad Ihsan Butt, Jamshed Nasir, Adnan Aslam, Asfand Fahad, Jarunee Soontharanon
Abstract
<abstract><p>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.</p></abstract>
Topics & Concepts
MathematicsHadamard transformType (biology)Differentiable functionKernel (algebra)Hermite polynomialsOperator (biology)Pure mathematicsFractional calculusConvex functionMathematical analysisRegular polygonGeometryBiochemistryRepressorChemistryGeneEcologyBiologyTranscription factorMathematical Inequalities and ApplicationsMathematical functions and polynomialsFractional Differential Equations Solutions