Open AccessJensen-Mercer variant of Hermite-Hadamard type inequalities via Atangana-Baleanu fractional operator
Author(s) -
JiaBao Liu,
Saad Ihsan Butt,
Jamshed Nasir,
Adnan Aslam,
Asfand Fahad,
Jarunee Soonthara
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022121
Subject(s) - mathematics , hadamard transform , type (biology) , differentiable function , kernel (algebra) , hermite polynomials , operator (biology) , pure mathematics , fractional calculus , convex function , mathematical analysis , regular polygon , geometry , chemistry , repressor , ecology , biochemistry , gene , transcription factor , biology
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.