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

Talib Hussain, Loredana Ciurdariu () and Eugenia Grecu ()
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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

Mathematics, 2024, vol. 12, issue 23, 1-27

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.

Keywords: generalized fractional integrals; Hermite–Hadamard inequality; Jensen–Mercer inequality; Hermite–Hadamard–Mercer inequality; Hölder’s inequality; power mean inequality; convex function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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