A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operator
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| Publicado en: | Journal of Inequalities and Applications vol. 2025, no. 1 (Dec 2025), p. 92 |
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Springer Nature B.V.
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| Acceso en línea: | Citation/Abstract Full Text Full Text - PDF |
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| 100 | 1 | |a Younis, Muhammad |u East China Normal University, School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, Shanghai, People’s Republic of China (GRID:grid.22069.3f) (ISNI:0000 0004 0369 6365) | |
| 245 | 1 | |a A new formulation of Hermite–Hadamard–Fejer inequalities connected with an extended fractional operator | |
| 260 | |b Springer Nature B.V. |c Dec 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a 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. | |
| 653 | |a Calculus | ||
| 653 | |a Fractional calculus | ||
| 653 | |a Inequalities | ||
| 653 | |a Operators (mathematics) | ||
| 653 | |a Integrals | ||
| 653 | |a Books | ||
| 653 | |a Integral equations | ||
| 700 | 1 | |a Liu, Zhi Guo |u East China Normal University, School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, Shanghai, People’s Republic of China (GRID:grid.22069.3f) (ISNI:0000 0004 0369 6365) | |
| 700 | 1 | |a Samraiz, Muhammad |u University of Sargodha, Muhammad Samraiz-Department of Mathematics, Sargodha, Pakistan (GRID:grid.412782.a) (ISNI:0000 0004 0609 4693) | |
| 700 | 1 | |a Mehmood, Ahsan |u East China Normal University, School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, Shanghai, People’s Republic of China (GRID:grid.22069.3f) (ISNI:0000 0004 0369 6365) | |
| 773 | 0 | |t Journal of Inequalities and Applications |g vol. 2025, no. 1 (Dec 2025), p. 92 | |
| 786 | 0 | |d ProQuest |t Advanced Technologies & Aerospace Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3236788301/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text |u https://www.proquest.com/docview/3236788301/fulltext/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3236788301/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |