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Fejér–Pachpatte–Mercer-Type Inequalities for Harmonically Convex Functions Involving Exponential Function in Kernel

Author

Listed:
  • Saad Ihsan Butt
  • Saba Yousaf
  • Khuram Ali Khan
  • Rostin Matendo Mabela
  • Abdullah M. Alsharif
  • Muhammad Shoaib Anwar

Abstract

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.

Suggested Citation

  • Saad Ihsan Butt & Saba Yousaf & Khuram Ali Khan & Rostin Matendo Mabela & Abdullah M. Alsharif & Muhammad Shoaib Anwar, 2022. "Fejér–Pachpatte–Mercer-Type Inequalities for Harmonically Convex Functions Involving Exponential Function in Kernel," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-19, March.
    • Handle: RePEc:hin:jnlmpe:7269033
    DOI: 10.1155/2022/7269033
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