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

• DOI: 10.3934/math.2022121
• Publication Date: 2021-11-08T10:31:29Z
• Authors: Jia-Bao Liu; ; Saad Ihsan Butt; Jamshed Nasir; Adnan Aslam; Asfand Fahad; Jarunee Soontharanon
• Keywords: Geometry; Operator (biology); Matrix Inequalities and Geometric Means; Mathematical analysis; Biochemistry; Gene; 01 natural sciences; Orthogonal Polynomials; Operator Inequalities; q-digamma function; Fractional Integrals; Differentiable function; Convex function; QA1-939; FOS: Mathematics; 0101 mathematics; Biology; Anomalous Diffusion Modeling and Analysis; Hadamard transform; convex function; atangana-baleanu fractional operators; Hermite polynomials; Ecology; Applied Mathematics; jensen-mercer inequality; Pure mathematics; Fractional calculus; Regular polygon; Fractional Derivatives; Chemistry; Modeling and Simulation; FOS: Biological sciences; Physical Sciences; Kernel (algebra); Repressor; Hermite-Hadamard Inequalities; Transcription factor; Type (biology); Mathematics

<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>