Hermite–jensen–mercer-type inequalities via caputo–fabrizio fractional integral for h-convex function

Miguel Vivas-Cortez; Muhammad Shoaib Saleem; Sana Sajid; Muhammad Sajid Zahoor; Artion Kashuri

doi:10.3390/fractalfract5040269

Hermite–jensen–mercer-type inequalities via caputo–fabrizio fractional integral for h-convex function

Miguel Vivas-Cortez^*
, Muhammad Shoaib Saleem
, Sana Sajid
, Muhammad Sajid Zahoor
, Artion Kashuri

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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.

Original language	English
Article number	269
Journal	Fractal and Fractional
Volume	5
Issue number	4
DOIs	https://doi.org/10.3390/fractalfract5040269
State	Published - 10 Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Funding

Funding: This research received external funding from Dirección de Investigción in Ponticial Catholic University of Ecuador. This research received external funding from Direcci?n de Investigci?n in Ponticial Catholic University of Ecuador.

Keywords

Caputo–Fabrizio fractional integral
Convex function
H-convex function
Hermite–Hadamard inequality
Hermite–Hadamard inequality
Jensen inequality
Jensen–Mercer inequality

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10.3390/fractalfract5040269

Cite this

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title = "Hermite–jensen–mercer-type inequalities via caputo–fabrizio fractional integral for h-convex function",

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 = "Caputo–Fabrizio fractional integral, Convex function, H-convex function, Hermite–Hadamard inequality, Hermite–Hadamard inequality, Jensen inequality, Jensen–Mercer inequality",

author = "Miguel Vivas-Cortez and Saleem, \{Muhammad Shoaib\} and Sana Sajid and Zahoor, \{Muhammad Sajid\} and Artion Kashuri",

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language = "English",

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T1 - Hermite–jensen–mercer-type inequalities via caputo–fabrizio fractional integral for h-convex function

AU - Vivas-Cortez, Miguel

AU - Saleem, Muhammad Shoaib

AU - Sajid, Sana

AU - Zahoor, Muhammad Sajid

AU - Kashuri, Artion

PY - 2021/12/10

Y1 - 2021/12/10

N2 - 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.

AB - 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.

KW - Caputo–Fabrizio fractional integral

KW - Convex function

KW - H-convex function

KW - Hermite–Hadamard inequality

KW - Jensen inequality

KW - Jensen–Mercer inequality

UR - https://www.scopus.com/pages/publications/85121328800

U2 - 10.3390/fractalfract5040269

DO - 10.3390/fractalfract5040269

M3 - Article

AN - SCOPUS:85121328800

SN - 2504-3110

VL - 5

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 4

M1 - 269

ER -

Hermite–jensen–mercer-type inequalities via caputo–fabrizio fractional integral for h-convex function

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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