LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities
Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called LR...
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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/243 |
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| author | Muhammad Bilal Khan Muhammad Aslam Noor Thabet Abdeljawad Abd Allah A. Mousa Bahaaeldin Abdalla Safar M. Alghamdi |
| author_facet | Muhammad Bilal Khan Muhammad Aslam Noor Thabet Abdeljawad Abd Allah A. Mousa Bahaaeldin Abdalla Safar M. Alghamdi |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called LR-preinvex interval-valued functions (LR-preinvex <i>I</i><i>-</i><i>V</i><i>-</i><i>Fs</i>) and to establish Hermite–Hadamard type inequalities for LR-preinvex <i>I</i><i>-</i><i>V</i><i>-</i><i>Fs</i> using partial order relation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>≤</mo><mi>p</mi></msub></mrow></semantics></math></inline-formula>). Furthermore, we demonstrate that our results include a large class of new and known inequalities for LR-preinvex interval-valued functions and their variant forms as special instances. Further, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions. |
| first_indexed | 2024-03-10T04:05:20Z |
| format | Article |
| id | doaj.art-5f65d5a1251e46f8a42dabc8e5903409 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:20Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-5f65d5a1251e46f8a42dabc8e59034092023-11-23T08:24:15ZengMDPI AGFractal and Fractional2504-31102021-11-015424310.3390/fractalfract5040243LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral InequalitiesMuhammad Bilal Khan0Muhammad Aslam Noor1Thabet Abdeljawad2Abd Allah A. Mousa3Bahaaeldin Abdalla4Safar M. Alghamdi5Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartment of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartment of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaConvexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called LR-preinvex interval-valued functions (LR-preinvex <i>I</i><i>-</i><i>V</i><i>-</i><i>Fs</i>) and to establish Hermite–Hadamard type inequalities for LR-preinvex <i>I</i><i>-</i><i>V</i><i>-</i><i>Fs</i> using partial order relation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>≤</mo><mi>p</mi></msub></mrow></semantics></math></inline-formula>). Furthermore, we demonstrate that our results include a large class of new and known inequalities for LR-preinvex interval-valued functions and their variant forms as special instances. Further, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.https://www.mdpi.com/2504-3110/5/4/243LR-preinvex interval-valued functionfractional integral operatorHermite-Hadamard type inequalityHermite-Hadamard Fejér type inequality |
| spellingShingle | Muhammad Bilal Khan Muhammad Aslam Noor Thabet Abdeljawad Abd Allah A. Mousa Bahaaeldin Abdalla Safar M. Alghamdi LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities Fractal and Fractional LR-preinvex interval-valued function fractional integral operator Hermite-Hadamard type inequality Hermite-Hadamard Fejér type inequality |
| title | LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities |
| title_full | LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities |
| title_fullStr | LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities |
| title_full_unstemmed | LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities |
| title_short | LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities |
| title_sort | lr preinvex interval valued functions and riemann liouville fractional integral inequalities |
| topic | LR-preinvex interval-valued function fractional integral operator Hermite-Hadamard type inequality Hermite-Hadamard Fejér type inequality |
| url | https://www.mdpi.com/2504-3110/5/4/243 |
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