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Volume 5
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Article

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

by
Miguel Vivas-Cortez
1,*,†,
Muhammad Shoaib Saleem
2,†,
Sana Sajid
2,†,
Muhammad Sajid Zahoor
2,† and
Artion Kashuri
3,†
1
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
2
Department of Mathematics, University of Okara, Okara 56300, Pakistan
3
Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 9401 Vlore, Albania
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Fractal Fract. 2021, 5(4), 269; https://doi.org/10.3390/fractalfract5040269
Submission received: 3 September 2021 / Revised: 16 November 2021 / Accepted: 25 November 2021 / Published: 10 December 2021
(This article belongs to the Special Issue Advances in Optimization and Nonlinear Analysis)
Versions Notes

Abstract

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.
Keywords: convex function; h-convex function; Hermite–Hadamard inequality; Caputo–Fabrizio fractional integral; Hermite–Hadamard inequality; Jensen inequality; Jensen–Mercer inequality convex function; h-convex function; Hermite–Hadamard inequality; Caputo–Fabrizio fractional integral; Hermite–Hadamard inequality; Jensen inequality; Jensen–Mercer inequality

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MDPI and ACS Style

Vivas-Cortez, M.; Saleem, M.S.; Sajid, S.; Zahoor, M.S.; Kashuri, A. Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Convex Function. Fractal Fract. 2021, 5, 269. https://doi.org/10.3390/fractalfract5040269

AMA Style

Vivas-Cortez M, Saleem MS, Sajid S, Zahoor MS, Kashuri A. Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Convex Function. Fractal and Fractional. 2021; 5(4):269. https://doi.org/10.3390/fractalfract5040269

Chicago/Turabian Style

Vivas-Cortez, Miguel, Muhammad Shoaib Saleem, Sana Sajid, Muhammad Sajid Zahoor, and Artion Kashuri. 2021. "Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Convex Function" Fractal and Fractional 5, no. 4: 269. https://doi.org/10.3390/fractalfract5040269

APA Style

Vivas-Cortez, M., Saleem, M. S., Sajid, S., Zahoor, M. S., & Kashuri, A. (2021). Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Convex Function. Fractal and Fractional, 5(4), 269. https://doi.org/10.3390/fractalfract5040269

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