Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications
Many scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown in popularity as a result of its capacity to quickly solve real-world problems. First, we establish new fractional inequalities of the Hadamard–...
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MDPI AG
2022-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/4/836 |
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| author | Soubhagya Kumar Sahoo Ravi P. Agarwal Pshtiwan Othman Mohammed Bibhakar Kodamasingh Kamsing Nonlaopon Khadijah M. Abualnaja |
| author_facet | Soubhagya Kumar Sahoo Ravi P. Agarwal Pshtiwan Othman Mohammed Bibhakar Kodamasingh Kamsing Nonlaopon Khadijah M. Abualnaja |
| author_sort | Soubhagya Kumar Sahoo |
| collection | DOAJ |
| description | Many scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown in popularity as a result of its capacity to quickly solve real-world problems. First, we establish new fractional inequalities of the Hadamard–Mercer, Pachpatte–Mercer, and Dragomir–Agarwal–Mercer types containing an exponential kernel. In this regard, the inequality proved by Jensen and Mercer plays a major role in our main results. Integral inequalities involving convexity have a wide range of applications in several domains of mathematics where symmetry is important. Both convexity and symmetry are closely linked with each other; when working on one of the topics, you can apply what you have learned to the other. We consider a new identity for differentiable mappings and present its companion bound for the Dragomir–Agarwal–Mercer type inequality employing a convex function. Applications involving matrices are presented. Finally, we conclude our article and discuss its future scope. |
| first_indexed | 2024-03-09T04:10:20Z |
| format | Article |
| id | doaj.art-18cec90e991c40679867fb3de33b5ec5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T04:10:20Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-18cec90e991c40679867fb3de33b5ec52023-12-03T14:00:46ZengMDPI AGSymmetry2073-89942022-04-0114483610.3390/sym14040836Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their ApplicationsSoubhagya Kumar Sahoo0Ravi P. Agarwal1Pshtiwan Othman Mohammed2Bibhakar Kodamasingh3Kamsing Nonlaopon4Khadijah M. Abualnaja5Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, IndiaDepartment of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USADepartment 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, IndiaDepartment of Mathematics, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaMany scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown in popularity as a result of its capacity to quickly solve real-world problems. First, we establish new fractional inequalities of the Hadamard–Mercer, Pachpatte–Mercer, and Dragomir–Agarwal–Mercer types containing an exponential kernel. In this regard, the inequality proved by Jensen and Mercer plays a major role in our main results. Integral inequalities involving convexity have a wide range of applications in several domains of mathematics where symmetry is important. Both convexity and symmetry are closely linked with each other; when working on one of the topics, you can apply what you have learned to the other. We consider a new identity for differentiable mappings and present its companion bound for the Dragomir–Agarwal–Mercer type inequality employing a convex function. Applications involving matrices are presented. Finally, we conclude our article and discuss its future scope.https://www.mdpi.com/2073-8994/14/4/836convex functionHadamard–Mercer inequalityPachpatte–Mercer inequalityfractional operatorexponential kernelmatrices |
| spellingShingle | Soubhagya Kumar Sahoo Ravi P. Agarwal Pshtiwan Othman Mohammed Bibhakar Kodamasingh Kamsing Nonlaopon Khadijah M. Abualnaja Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications Symmetry convex function Hadamard–Mercer inequality Pachpatte–Mercer inequality fractional operator exponential kernel matrices |
| title | Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications |
| title_full | Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications |
| title_fullStr | Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications |
| title_full_unstemmed | Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications |
| title_short | Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications |
| title_sort | hadamard mercer dragomir agarwal mercer and pachpatte mercer type fractional inclusions for convex functions with an exponential kernel and their applications |
| topic | convex function Hadamard–Mercer inequality Pachpatte–Mercer inequality fractional operator exponential kernel matrices |
| url | https://www.mdpi.com/2073-8994/14/4/836 |
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