Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation
The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have em...
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MDPI AG
2022-01-01
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| author | Muhammad Bilal Khan Hatim Ghazi Zaini Savin Treanțǎ Mohamed S. Soliman Kamsing Nonlaopon |
| author_facet | Muhammad Bilal Khan Hatim Ghazi Zaini Savin Treanțǎ Mohamed S. Soliman Kamsing Nonlaopon |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (<i>I</i>-<i>V</i>·<i>Fs</i>), known as left and right <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula>-pre-invex interval-valued functions (LR-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula>-pre-invex <i>I</i>-<i>V</i>·<i>Fs</i>). For this class of non-convex <i>I</i>-<i>V</i>·<i>Fs</i>, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings. |
| first_indexed | 2024-03-10T01:01:15Z |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:01:15Z |
| publishDate | 2022-01-01 |
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| series | Mathematics |
| spelling | doaj.art-1874ff7f42ee4d18a55601726018b2e82023-11-23T14:33:55ZengMDPI AGMathematics2227-73902022-01-0110220410.3390/math10020204Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order RelationMuhammad Bilal Khan0Hatim Ghazi Zaini1Savin Treanțǎ2Mohamed S. Soliman3Kamsing Nonlaopon4Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, PakistanDepartment of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaDepartment of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandThe concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (<i>I</i>-<i>V</i>·<i>Fs</i>), known as left and right <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula>-pre-invex interval-valued functions (LR-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula>-pre-invex <i>I</i>-<i>V</i>·<i>Fs</i>). For this class of non-convex <i>I</i>-<i>V</i>·<i>Fs</i>, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings.https://www.mdpi.com/2227-7390/10/2/204LR-<i>χ</i>-pre-invex interval-valued functioninterval Riemann–Liouville fractional integral operatorHermite–Hadamard inequalityHermite–Hadamard Fejér inequality |
| spellingShingle | Muhammad Bilal Khan Hatim Ghazi Zaini Savin Treanțǎ Mohamed S. Soliman Kamsing Nonlaopon Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation Mathematics LR-<i>χ</i>-pre-invex interval-valued function interval Riemann–Liouville fractional integral operator Hermite–Hadamard inequality Hermite–Hadamard Fejér inequality |
| title | Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation |
| title_full | Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation |
| title_fullStr | Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation |
| title_full_unstemmed | Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation |
| title_short | Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation |
| title_sort | riemann liouville fractional integral inequalities for generalized pre invex functions of interval valued settings based upon pseudo order relation |
| topic | LR-<i>χ</i>-pre-invex interval-valued function interval Riemann–Liouville fractional integral operator Hermite–Hadamard inequality Hermite–Hadamard Fejér inequality |
| url | https://www.mdpi.com/2227-7390/10/2/204 |
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