Fejér–Pachpatte–Mercer-Type Inequalities for Harmonically Convex Functions Involving Exponential Function in Kernel
In the present study, fractional variants of Hermite–Hadamard, Hermite–Hadamard–Fejér, and Pachpatte inequalities are studied by employing Mercer concept. Firstly, new Hermite–Hadamard–Mercer-type inequalities are presented for harmonically convex functions involving fractional integral operators wi...
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| Veröffentlicht in: | Mathematical problems in engineering 2022-03, Vol.2022, p.1-19 |
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| container_title | Mathematical problems in engineering |
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| creator | Butt, Saad Ihsan Yousaf, Saba Khan, Khuram Ali Matendo Mabela, Rostin Alsharif, Abdullah M. |
| description | In the present study, fractional variants of Hermite–Hadamard, Hermite–Hadamard–Fejér, and Pachpatte inequalities are studied by employing Mercer concept. Firstly, new Hermite–Hadamard–Mercer-type inequalities are presented for harmonically convex functions involving fractional integral operators with exponential kernel. Then, weighted Hadamard–Fejér–Mercer-type inequalities involving exponential function as kernel are proved. Finally, Pachpatte–Mercer-type inequalities for products of harmonically convex functions via fractional integral operators with exponential kernel are constructed. |
| doi_str_mv | 10.1155/2022/7269033 |
| format | Article |
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Firstly, new Hermite–Hadamard–Mercer-type inequalities are presented for harmonically convex functions involving fractional integral operators with exponential kernel. Then, weighted Hadamard–Fejér–Mercer-type inequalities involving exponential function as kernel are proved. 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This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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| subjects | Approximation Calculus Convex analysis Engineering Exponential functions Fractional calculus Inequalities Information theory Kernels Numerical analysis Operators (mathematics) Science |
| title | Fejér–Pachpatte–Mercer-Type Inequalities for Harmonically Convex Functions Involving Exponential Function in Kernel |
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