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A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions

Author

Listed:
  • Talib Hussain

    (Department of Mathematics and Statistics, University of Agriculture Faisalabad, Faisalabad 38000, Pakistan)

  • Loredana Ciurdariu

    (Department of Mathematics, Politehnica University of Timișoara, 300006 Timisoara, Romania)

  • Eugenia Grecu

    (Department of Management, Politehnica University of Timișoara, 300006 Timisoara, Romania)

Abstract

The goal of this study is to develop numerous Hermite–Hadamard–Mercer (H–H–M)-type inequalities involving various fractional integral operators, including classical, Riemann–Liouville (R.L), k-Riemann–Liouville (k-R.L), and their generalized fractional integral operators. In addition, we establish a number of corresponding fractional integral inequalities for three-times differentiable convex functions that are connected to the right side of the H–H–M-type inequality. For these results, further remarks and observations are provided. Following that, a couple of graphical representations are shown to highlight the key findings of our study. Finally, some applications on special means are shown to demonstrate the effectiveness of our inequalities.

Suggested Citation

  • Talib Hussain & Loredana Ciurdariu & Eugenia Grecu, 2024. "A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions," Mathematics, MDPI, vol. 12(23), pages 1-27, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3711-:d:1530151
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    References listed on IDEAS

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    1. Thanin Sitthiwirattham & Miguel Vivas-Cortez & Muhammad Aamir Ali & Hãœseyin Budak & Ä°Brahim Avci, 2024. "A Study Of Fractional Hermite–Hadamard–Mercer Inequalities For Differentiable Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-13.
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