Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for <i>h</i>-Convex Stochastic Process via Interval-Valued Functions
Mathematical programming and optimization problems related to fluid dynamics are heavily influenced by stochastic processes associated with integral and variational inequalities. Furthermore, symmetry and convexity are intrinsically related. Over the last few years, both have become increasingly int...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/4/831 |
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| author | Waqar Afzal Evgeniy Yu. Prosviryakov Sheza M. El-Deeb Yahya Almalki |
| author_facet | Waqar Afzal Evgeniy Yu. Prosviryakov Sheza M. El-Deeb Yahya Almalki |
| author_sort | Waqar Afzal |
| collection | DOAJ |
| description | Mathematical programming and optimization problems related to fluid dynamics are heavily influenced by stochastic processes associated with integral and variational inequalities. Furthermore, symmetry and convexity are intrinsically related. Over the last few years, both have become increasingly interconnected so that we can learn from one and apply it to the other. The objective of this note is to convert ordinary stochastic processes into interval stochastic processes due to the wide range of applications in various disciplines. We have developed Hermite–Hadamard (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">H</mi><mo>.</mo><mi mathvariant="double-struck">H</mi></mrow></semantics></math></inline-formula>), Ostrowski-, and Jensen-type inequalities using interval <i>h</i>-convex stochastic processes. Our main results can be applied to a variety of new and well-known outcomes as specific situations. The results of this study are expected to stimulate future research on inequalities using fractional and fuzzy integral operators. Furthermore, we validate our main findings by providing some non-trivial examples. To demonstrate their general properties, we illustrate the connections between the examined results and those that have already been published. The results discussed in this article can be seen as improvements and refinements to results that have already been published. This is a fascinating subject that can be investigated in the future to identify equivalent inequalities for various convexity types. |
| first_indexed | 2024-03-11T04:29:38Z |
| format | Article |
| id | doaj.art-f8fae02fe4e046ba89a91decf2825f0a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T04:29:38Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f8fae02fe4e046ba89a91decf2825f0a2023-11-17T21:33:21ZengMDPI AGSymmetry2073-89942023-03-0115483110.3390/sym15040831Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for <i>h</i>-Convex Stochastic Process via Interval-Valued FunctionsWaqar Afzal0Evgeniy Yu. Prosviryakov1Sheza M. El-Deeb2Yahya Almalki3Department of Mathematics, University of Gujrat, Gujrat 50700, PakistanSector of Nonlinear Vortex Hydrodynamics, Institute of Engineering Science UB RAS, 620049 Ekaterinburg, RussiaDepartment of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, EgyptDepartment of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi ArabiaMathematical programming and optimization problems related to fluid dynamics are heavily influenced by stochastic processes associated with integral and variational inequalities. Furthermore, symmetry and convexity are intrinsically related. Over the last few years, both have become increasingly interconnected so that we can learn from one and apply it to the other. The objective of this note is to convert ordinary stochastic processes into interval stochastic processes due to the wide range of applications in various disciplines. We have developed Hermite–Hadamard (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">H</mi><mo>.</mo><mi mathvariant="double-struck">H</mi></mrow></semantics></math></inline-formula>), Ostrowski-, and Jensen-type inequalities using interval <i>h</i>-convex stochastic processes. Our main results can be applied to a variety of new and well-known outcomes as specific situations. The results of this study are expected to stimulate future research on inequalities using fractional and fuzzy integral operators. Furthermore, we validate our main findings by providing some non-trivial examples. To demonstrate their general properties, we illustrate the connections between the examined results and those that have already been published. The results discussed in this article can be seen as improvements and refinements to results that have already been published. This is a fascinating subject that can be investigated in the future to identify equivalent inequalities for various convexity types.https://www.mdpi.com/2073-8994/15/4/831Hermite–Hadamard inequalityOstrowski inequalityJensen inequalitystochastic processinterval-valued functionsstochastic systems |
| spellingShingle | Waqar Afzal Evgeniy Yu. Prosviryakov Sheza M. El-Deeb Yahya Almalki Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for <i>h</i>-Convex Stochastic Process via Interval-Valued Functions Symmetry Hermite–Hadamard inequality Ostrowski inequality Jensen inequality stochastic process interval-valued functions stochastic systems |
| title | Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for <i>h</i>-Convex Stochastic Process via Interval-Valued Functions |
| title_full | Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for <i>h</i>-Convex Stochastic Process via Interval-Valued Functions |
| title_fullStr | Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for <i>h</i>-Convex Stochastic Process via Interval-Valued Functions |
| title_full_unstemmed | Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for <i>h</i>-Convex Stochastic Process via Interval-Valued Functions |
| title_short | Some New Estimates of Hermite–Hadamard, Ostrowski and Jensen-Type Inclusions for <i>h</i>-Convex Stochastic Process via Interval-Valued Functions |
| title_sort | some new estimates of hermite hadamard ostrowski and jensen type inclusions for i h i convex stochastic process via interval valued functions |
| topic | Hermite–Hadamard inequality Ostrowski inequality Jensen inequality stochastic process interval-valued functions stochastic systems |
| url | https://www.mdpi.com/2073-8994/15/4/831 |
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