New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators
The objective of the current article is to incorporate the concepts of convexity and Jensen-Mercer inequality with the Caputo-Fabrizio fractional integral operator. Moreover, we present new midpoint versions of Hermite-Hadamard-Mercer (H-H-M) type inequalities for convex functions and the product of...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-02-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016822006755 |
| _version_ | 1811163525206245376 |
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| author | Soubhagya Kumar Sahoo Y.S. Hamed Pshtiwan Othman Mohammed Bibhakar Kodamasingh Kamsing Nonlaopon |
| author_facet | Soubhagya Kumar Sahoo Y.S. Hamed Pshtiwan Othman Mohammed Bibhakar Kodamasingh Kamsing Nonlaopon |
| author_sort | Soubhagya Kumar Sahoo |
| collection | DOAJ |
| description | The objective of the current article is to incorporate the concepts of convexity and Jensen-Mercer inequality with the Caputo-Fabrizio fractional integral operator. Moreover, we present new midpoint versions of Hermite-Hadamard-Mercer (H-H-M) type inequalities for convex functions and the product of two convex functions on fractional integrals. Also, we consider a new identity for differentiable mappings in the context of the Caputo-Fabrizio fractional integral operators. Then, considering this identity as an auxiliary result, some new related H-H-M type inequality with the assistance of Hölder, power-mean, Young, and Hölder-İşcan inequality are presented. Finally, we give some applications of modified Bessel functions and matrices, and we also discuss some future scopes. |
| first_indexed | 2024-04-10T15:06:37Z |
| format | Article |
| id | doaj.art-9e9eef5583da488abea5464f58d9e00c |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-10T15:06:37Z |
| publishDate | 2023-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-9e9eef5583da488abea5464f58d9e00c2023-02-15T04:27:05ZengElsevierAlexandria Engineering Journal1110-01682023-02-0165689698New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operatorsSoubhagya Kumar Sahoo0Y.S. Hamed1Pshtiwan Othman Mohammed2Bibhakar Kodamasingh3Kamsing Nonlaopon4Department of Mathematics, Institute of Technical Education and Research, Siksha ’O’ Anusandhan University, Bhubaneswar 751030, Odisha, IndiaDepartment of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, IraqDepartment of Mathematics, Institute of Technical Education and Research, Siksha ’O’ Anusandhan University, Bhubaneswar 751030, Odisha, IndiaDepartment of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand; Corresponding author.The objective of the current article is to incorporate the concepts of convexity and Jensen-Mercer inequality with the Caputo-Fabrizio fractional integral operator. Moreover, we present new midpoint versions of Hermite-Hadamard-Mercer (H-H-M) type inequalities for convex functions and the product of two convex functions on fractional integrals. Also, we consider a new identity for differentiable mappings in the context of the Caputo-Fabrizio fractional integral operators. Then, considering this identity as an auxiliary result, some new related H-H-M type inequality with the assistance of Hölder, power-mean, Young, and Hölder-İşcan inequality are presented. Finally, we give some applications of modified Bessel functions and matrices, and we also discuss some future scopes.http://www.sciencedirect.com/science/article/pii/S1110016822006755Hermite-Hadamard-Mercer inequalityCaputo-Fabrizio operatorHölder’s inequalityHölder-İşcan inequalityModified Bessel functions |
| spellingShingle | Soubhagya Kumar Sahoo Y.S. Hamed Pshtiwan Othman Mohammed Bibhakar Kodamasingh Kamsing Nonlaopon New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators Alexandria Engineering Journal Hermite-Hadamard-Mercer inequality Caputo-Fabrizio operator Hölder’s inequality Hölder-İşcan inequality Modified Bessel functions |
| title | New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators |
| title_full | New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators |
| title_fullStr | New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators |
| title_full_unstemmed | New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators |
| title_short | New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators |
| title_sort | new midpoint type hermite hadamard mercer inequalities pertaining to caputo fabrizio fractional operators |
| topic | Hermite-Hadamard-Mercer inequality Caputo-Fabrizio operator Hölder’s inequality Hölder-İşcan inequality Modified Bessel functions |
| url | http://www.sciencedirect.com/science/article/pii/S1110016822006755 |
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