Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order Relation
The relevance of convex and non-convex functions in optimization research is well known. Due to the behavior of its definition, the idea of convexity also plays a major role in the subject of inequalities. The main concern of this paper is to establish new integral inequalities for newly defined lef...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/3/473 |
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| author | Muhammad Bilal Khan Hari Mohan Srivastava Pshtiwan Othman Mohammed Kamsing Nonlaopon Yasser S. Hamed |
| author_facet | Muhammad Bilal Khan Hari Mohan Srivastava Pshtiwan Othman Mohammed Kamsing Nonlaopon Yasser S. Hamed |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | The relevance of convex and non-convex functions in optimization research is well known. Due to the behavior of its definition, the idea of convexity also plays a major role in the subject of inequalities. The main concern of this paper is to establish new integral inequalities for newly defined left and right convex interval-valued function on coordinates through pseudo order relation and double integral. Some of the Hermite–Hadamard type inequalities for the product of two left and right convex interval-valued functions on coordinates are also obtained. Moreover, Hermite–Hadamard–Fejér type inequalities are also derived for left and right convex interval-valued functions on coordinates. Some useful examples are also presented to prove the validity of this study. The proved results of this paper are generalizations of many known results, which are proved by Dragomir, Latif et al. and Zhao, and can be vied as applications of this study. |
| first_indexed | 2024-03-09T12:25:37Z |
| format | Article |
| id | doaj.art-4267d7fef1894805a6f7610bede75cc7 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T12:25:37Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4267d7fef1894805a6f7610bede75cc72023-11-30T22:35:07ZengMDPI AGSymmetry2073-89942022-02-0114347310.3390/sym14030473Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order RelationMuhammad Bilal Khan0Hari Mohan Srivastava1Pshtiwan Othman Mohammed2Kamsing Nonlaopon3Yasser S. Hamed4Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, IraqDepartment 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 ArabiaThe relevance of convex and non-convex functions in optimization research is well known. Due to the behavior of its definition, the idea of convexity also plays a major role in the subject of inequalities. The main concern of this paper is to establish new integral inequalities for newly defined left and right convex interval-valued function on coordinates through pseudo order relation and double integral. Some of the Hermite–Hadamard type inequalities for the product of two left and right convex interval-valued functions on coordinates are also obtained. Moreover, Hermite–Hadamard–Fejér type inequalities are also derived for left and right convex interval-valued functions on coordinates. Some useful examples are also presented to prove the validity of this study. The proved results of this paper are generalizations of many known results, which are proved by Dragomir, Latif et al. and Zhao, and can be vied as applications of this study.https://www.mdpi.com/2073-8994/14/3/473double integralleft and right convex interval-valued function on coordinatesHermite–Hadamard inequalityHermite–Hadamard–Fejér inequality |
| spellingShingle | Muhammad Bilal Khan Hari Mohan Srivastava Pshtiwan Othman Mohammed Kamsing Nonlaopon Yasser S. Hamed Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order Relation Symmetry double integral left and right convex interval-valued function on coordinates Hermite–Hadamard inequality Hermite–Hadamard–Fejér inequality |
| title | Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order Relation |
| title_full | Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order Relation |
| title_fullStr | Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order Relation |
| title_full_unstemmed | Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order Relation |
| title_short | Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order Relation |
| title_sort | some new estimates on coordinates of left and right convex interval valued functions based on pseudo order relation |
| topic | double integral left and right convex interval-valued function on coordinates Hermite–Hadamard inequality Hermite–Hadamard–Fejér inequality |
| url | https://www.mdpi.com/2073-8994/14/3/473 |
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