Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications
Abstract
:1. Introduction
2. Preliminaries
3. Hadamard–Jensen–Mercer- and Pachpatte–Mercer-Type Inequalities via Fractional Integrals
Pachpatte–Mercer-Type Fractional Inequality
4. New Fractional Inequalities of Dragomir–Agarwal–Mercer-Type
5. Applications
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
H–H | Hermite–Hadamard |
R–L | Riemann–Liouville |
J–M | Jensen–Mercer |
H–H–M | Hermite–Hadamard–Mercer |
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Sahoo, S.K.; Agarwal, R.P.; Mohammed, P.O.; Kodamasingh, B.; Nonlaopon, K.; Abualnaja, K.M. Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications. Symmetry 2022, 14, 836. https://doi.org/10.3390/sym14040836
Sahoo SK, Agarwal RP, Mohammed PO, Kodamasingh B, Nonlaopon K, Abualnaja KM. Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications. Symmetry. 2022; 14(4):836. https://doi.org/10.3390/sym14040836
Chicago/Turabian StyleSahoo, Soubhagya Kumar, Ravi P. Agarwal, Pshtiwan Othman Mohammed, Bibhakar Kodamasingh, Kamsing Nonlaopon, and Khadijah M. Abualnaja. 2022. "Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications" Symmetry 14, no. 4: 836. https://doi.org/10.3390/sym14040836
APA StyleSahoo, S. K., Agarwal, R. P., Mohammed, P. O., Kodamasingh, B., Nonlaopon, K., & Abualnaja, K. M. (2022). Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications. Symmetry, 14(4), 836. https://doi.org/10.3390/sym14040836