New Generalized Class of Convex Functions and Some Related Integral Inequalities
There is a strong correlation between convexity and symmetry concepts. In this study, we investigated the new generic class of functions called the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>...
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| Format: | Article |
| Language: | English |
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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/2073-8994/14/4/722 |
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| author | Artion Kashuri Ravi P. Agarwal Pshtiwan Othman Mohammed Kamsing Nonlaopon Khadijah M. Abualnaja Yasser S. Hamed |
| author_facet | Artion Kashuri Ravi P. Agarwal Pshtiwan Othman Mohammed Kamsing Nonlaopon Khadijah M. Abualnaja Yasser S. Hamed |
| author_sort | Artion Kashuri |
| collection | DOAJ |
| description | There is a strong correlation between convexity and symmetry concepts. In this study, we investigated the new generic class of functions called the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>–generalized convex and studied its basic algebraic properties. The Hermite–Hadamard inequality for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>–generalized convex function, for the products of two functions and of this type, were proven. Moreover, this class of functions was applied to several known identities; midpoint-type inequalities of Ostrowski and Simpson were derived. Our results are extensions of many previous contributions related to integral inequalities via different convexities. |
| first_indexed | 2024-03-09T10:28:04Z |
| format | Article |
| id | doaj.art-53ee1ea80f0b4eb0be93a649196a773c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T10:28:04Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-53ee1ea80f0b4eb0be93a649196a773c2023-12-01T21:28:31ZengMDPI AGSymmetry2073-89942022-04-0114472210.3390/sym14040722New Generalized Class of Convex Functions and Some Related Integral InequalitiesArtion Kashuri0Ravi P. Agarwal1Pshtiwan Othman Mohammed2Kamsing Nonlaopon3Khadijah M. Abualnaja4Yasser S. Hamed5Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”, 9400 Vlora, AlbaniaDepartment of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USADepartment of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, IraqDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaThere is a strong correlation between convexity and symmetry concepts. In this study, we investigated the new generic class of functions called the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>–generalized convex and studied its basic algebraic properties. The Hermite–Hadamard inequality for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>–generalized convex function, for the products of two functions and of this type, were proven. Moreover, this class of functions was applied to several known identities; midpoint-type inequalities of Ostrowski and Simpson were derived. Our results are extensions of many previous contributions related to integral inequalities via different convexities.https://www.mdpi.com/2073-8994/14/4/722Hermite–Hadamard inequalityOstrowski inequalitySimpson inequality(<i>n</i>,<i>m</i>)–generalized convexity |
| spellingShingle | Artion Kashuri Ravi P. Agarwal Pshtiwan Othman Mohammed Kamsing Nonlaopon Khadijah M. Abualnaja Yasser S. Hamed New Generalized Class of Convex Functions and Some Related Integral Inequalities Symmetry Hermite–Hadamard inequality Ostrowski inequality Simpson inequality (<i>n</i>,<i>m</i>)–generalized convexity |
| title | New Generalized Class of Convex Functions and Some Related Integral Inequalities |
| title_full | New Generalized Class of Convex Functions and Some Related Integral Inequalities |
| title_fullStr | New Generalized Class of Convex Functions and Some Related Integral Inequalities |
| title_full_unstemmed | New Generalized Class of Convex Functions and Some Related Integral Inequalities |
| title_short | New Generalized Class of Convex Functions and Some Related Integral Inequalities |
| title_sort | new generalized class of convex functions and some related integral inequalities |
| topic | Hermite–Hadamard inequality Ostrowski inequality Simpson inequality (<i>n</i>,<i>m</i>)–generalized convexity |
| url | https://www.mdpi.com/2073-8994/14/4/722 |
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