Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Convex Function

Fractal and Fractional

Artion Kashuri¹  Sana Sajid²  Muhammad Sajid Zahoor²  Muhammad Shoaib Saleem²  Miguel Vivas-Cortez³ 

[1] Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 9401 Vlore, Albania;Department of Mathematics, University of Okara, Okara 56300, Pakistan;Faculty of Exact and Natural Sciences, School of Physical and Mathematical Sciences, Pontificia Universidad Católica del Ecuador, Av. 12 October 1076, Quito 17-01-2184, Ecuador;

关键词: convex function;    h-convex function;    Hermite–Hadamard inequality;    Caputo–Fabrizio fractional integral;    Hermite–Hadamard inequality;    Jensen inequality;   

DOI  :  10.3390/fractalfract5040269

来源: DOAJ

【 摘 要 】

Integral inequalities involving many fractional integral operators are used to solve various fractional differential equations. In the present paper, we will generalize the Hermite–Jensen–Mercer-type inequalities for an h-convex function via a Caputo–Fabrizio fractional integral. We develop some novel Caputo–Fabrizio fractional integral inequalities. We also present Caputo–Fabrizio fractional integral identities for differentiable mapping, and these will be used to give estimates for some fractional Hermite–Jensen–Mercer-type inequalities. Some familiar results are recaptured as special cases of our results.

【 授权许可】

Unknown