Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems
Due to applicability of mathematical inequalities in control systems, actuarial science, information theory and its utilization in other sciences, several researchers are inclined to prove their refinements and generalizations. In the study of mathematical inequalities, convex functions (CFs) and th...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824014911 |
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| author | Asfand Fahad Zammad Ali Shigeru Furuichi Yuanheng Wang |
| author_facet | Asfand Fahad Zammad Ali Shigeru Furuichi Yuanheng Wang |
| author_sort | Asfand Fahad |
| collection | DOAJ |
| description | Due to applicability of mathematical inequalities in control systems, actuarial science, information theory and its utilization in other sciences, several researchers are inclined to prove their refinements and generalizations. In the study of mathematical inequalities, convex functions (CFs) and the derived classes of CFs are the most studied objects. On the other hand, fractional calculus has emerged as an indispensable tool in Engineering, Physics, and Mathematics, with widespread applications. The recently introduced Cr-order based class of interval-valued functions (IVFs) has shown applications in information theory. In this paper, we aim to investigate mathematical inequalities for geometrically arithmetically Cr-convex functions (GA-Cr-CFs) via interval-valued Hadamard fractional integral operators (IVHFIOs). More precisely, we study the Hermite–Hadamard–Mercer type inequalities and the weighted Hermite–Hadamard–Mercer type inequalities involving GA-Cr-CFs and IVHFIOs. Under particular assumptions, the proved results produce inequalities from the recent related literature. Furthermore, we establish connections between geometrically arithmetically convex functions (GA-CFs) and self information function of each event with a given probability in a complete information system. At the end, we demonstrate the role of fractional order of IVHFIOs in producing the refinements of the inequalities for the usual integrals. Thus, the current study provides both the extension of theoretical literature as well as application aspects. |
| format | Article |
| id | doaj-art-05200b7cd0914db997d4381c8da33d02 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-05200b7cd0914db997d4381c8da33d022025-02-07T04:47:06ZengElsevierAlexandria Engineering Journal1110-01682025-02-01113509515Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systemsAsfand Fahad0Zammad Ali1Shigeru Furuichi2Yuanheng Wang3School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, China; Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, 6000, PakistanCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, 6000, PakistanDepartment of Information Science, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo, 1540000, Japan; Department of Mathematics, Saveetha School of Engineering, SIMATS, Thandalam, Chennai, 602105, Tamilnadu, IndiaSchool of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, China; Corresponding author.Due to applicability of mathematical inequalities in control systems, actuarial science, information theory and its utilization in other sciences, several researchers are inclined to prove their refinements and generalizations. In the study of mathematical inequalities, convex functions (CFs) and the derived classes of CFs are the most studied objects. On the other hand, fractional calculus has emerged as an indispensable tool in Engineering, Physics, and Mathematics, with widespread applications. The recently introduced Cr-order based class of interval-valued functions (IVFs) has shown applications in information theory. In this paper, we aim to investigate mathematical inequalities for geometrically arithmetically Cr-convex functions (GA-Cr-CFs) via interval-valued Hadamard fractional integral operators (IVHFIOs). More precisely, we study the Hermite–Hadamard–Mercer type inequalities and the weighted Hermite–Hadamard–Mercer type inequalities involving GA-Cr-CFs and IVHFIOs. Under particular assumptions, the proved results produce inequalities from the recent related literature. Furthermore, we establish connections between geometrically arithmetically convex functions (GA-CFs) and self information function of each event with a given probability in a complete information system. At the end, we demonstrate the role of fractional order of IVHFIOs in producing the refinements of the inequalities for the usual integrals. Thus, the current study provides both the extension of theoretical literature as well as application aspects.http://www.sciencedirect.com/science/article/pii/S1110016824014911GA-Cr-convex functionsSelf information functionComplete event systemHermite–Hadamard–Mercer inequalitiesInterval-valued Hadamard fractional integral operators |
| spellingShingle | Asfand Fahad Zammad Ali Shigeru Furuichi Yuanheng Wang Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems Alexandria Engineering Journal GA-Cr-convex functions Self information function Complete event system Hermite–Hadamard–Mercer inequalities Interval-valued Hadamard fractional integral operators |
| title | Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems |
| title_full | Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems |
| title_fullStr | Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems |
| title_full_unstemmed | Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems |
| title_short | Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems |
| title_sort | novel fractional integral inequalities for ga cr convex functions and connections with information systems |
| topic | GA-Cr-convex functions Self information function Complete event system Hermite–Hadamard–Mercer inequalities Interval-valued Hadamard fractional integral operators |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824014911 |
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