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
Hauptverfasser: Butt, Saad Ihsan, Yousaf, Saba, Khan, Khuram Ali, Matendo Mabela, Rostin, Alsharif, Abdullah M.
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Sprache:eng
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Zusammenfassung: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2022/7269033