Some New Hermite–Hadamard–Type Inequalities Using the Erdélyi–Kober Fractional Integral Operator for Mappings Defined on Harmonic Sets With Applications to Error Estimates of Numerical Integration Formulas
Yahya Almalki, Waqar Afzal, Najla M. Aloraini, Ahmad Albaity, Joshua Kiddy K. Asamoah
Source abstract
In this work, we establish several new variants of the Hermite–Hadamard integral inequality, together with various product‐type extensions, by employing the Erdélyi–Kober fractional integral operator for mappings defined on harmonic sets. To demonstrate the validity and effectiveness of the obtained results, we present nontrivial numerical examples supported by graphical illustrations and tabulated comparisons for different choices of the fractional parameters. Furthermore, as an application of our main results, we derive explicit error estimates for the trapezoidal rule on harmonic intervals.
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