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On Hermite–Hadamard–Fejér-Type Inequalities for η -Convex Functions via Quantum Calculus

Author

Listed:
  • Nuttapong Arunrat

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Hüseyin Budak

    (Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey)

Abstract

In this paper, we use q a - and q b -integrals to establish some quantum Hermite–Hadamard–Fejér-type inequalities for η -convex functions. By taking q → 1 , our results reduce to classical results on Hermite–Hadamard–Fejér-type inequalities for η -convex functions. Moreover, we give some examples for quantum Hermite–Hadamard–Fejér-type inequalities for η -convex functions. Some results presented here for η -convex functions provide extensions of others given in earlier works for convex and η -convex functions.

Suggested Citation

  • Nuttapong Arunrat & Kamsing Nonlaopon & Hüseyin Budak, 2023. "On Hermite–Hadamard–Fejér-Type Inequalities for η -Convex Functions via Quantum Calculus," Mathematics, MDPI, vol. 11(15), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3387-:d:1209312
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