A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operator
Abstract In this work, we classify the extensions of Hermite–Hadamard(H–H)–Fejer-type inequalities for the fractional operators involving nonlinear kernel. By utilizing these inequalities, we develop many kinds of fractional integral (FI) inequalities. By considering the limiting cases of our main r...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-08-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03342-2 |
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| author | Muhammad Younis Zhi Guo Liu Muhammad Samraiz Ahsan Mehmood |
| author_facet | Muhammad Younis Zhi Guo Liu Muhammad Samraiz Ahsan Mehmood |
| author_sort | Muhammad Younis |
| collection | DOAJ |
| description | Abstract In this work, we classify the extensions of Hermite–Hadamard(H–H)–Fejer-type inequalities for the fractional operators involving nonlinear kernel. By utilizing these inequalities, we develop many kinds of fractional integral (FI) inequalities. By considering the limiting cases of our main results, we attain the inequalities that already exist in the literature. In our work, we calculate the bounds of well-known fractional problems involving extended fractional operators. As implementations of the proved results, we calculate the midpoint-type inequalities. In the last section as the application of our defined operator, we present a generalized Abel integral equation and compute its solution. Also, we define the nonlinear form of a weakly singular Volterra-type integral equation and investigate its solution. These results might be useful in the investigation of the uniqueness of mathematical models and applied problems. |
| format | Article |
| id | doaj-art-aa564f67b94647d19ca08d3f65bd33c8 |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-aa564f67b94647d19ca08d3f65bd33c82025-08-20T03:46:28ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-08-012025112110.1186/s13660-025-03342-2A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operatorMuhammad Younis0Zhi Guo Liu1Muhammad Samraiz2Ahsan Mehmood3School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal UniversitySchool of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal UniversityMuhammad Samraiz-Department of Mathematics, University of SargodhaSchool of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal UniversityAbstract In this work, we classify the extensions of Hermite–Hadamard(H–H)–Fejer-type inequalities for the fractional operators involving nonlinear kernel. By utilizing these inequalities, we develop many kinds of fractional integral (FI) inequalities. By considering the limiting cases of our main results, we attain the inequalities that already exist in the literature. In our work, we calculate the bounds of well-known fractional problems involving extended fractional operators. As implementations of the proved results, we calculate the midpoint-type inequalities. In the last section as the application of our defined operator, we present a generalized Abel integral equation and compute its solution. Also, we define the nonlinear form of a weakly singular Volterra-type integral equation and investigate its solution. These results might be useful in the investigation of the uniqueness of mathematical models and applied problems.https://doi.org/10.1186/s13660-025-03342-2Convex FunctionHermiteHadamardFejerModified ( k , s ) $(k,s)$ -fractional operator |
| spellingShingle | Muhammad Younis Zhi Guo Liu Muhammad Samraiz Ahsan Mehmood A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operator Journal of Inequalities and Applications Convex Function Hermite Hadamard Fejer Modified ( k , s ) $(k,s)$ -fractional operator |
| title | A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operator |
| title_full | A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operator |
| title_fullStr | A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operator |
| title_full_unstemmed | A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operator |
| title_short | A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operator |
| title_sort | new formulation of hermite hadamard fejer inequalities connected with an extended fractional operator |
| topic | Convex Function Hermite Hadamard Fejer Modified ( k , s ) $(k,s)$ -fractional operator |
| url | https://doi.org/10.1186/s13660-025-03342-2 |
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