A Unified Sharp Integral Inequality With Applications to Trapezoid, Mid-Point, and Simpson-Type Inequalities

Mohsen Rostamian Delavar and Mohsen Kian

Journal of Mathematics, 2026, vol. 2026, 1-10

Abstract: In this paper, we established a sharp integral inequality involving the Chebyshev functional and the average of Riemann integrable functions. Our main result furnishes a refined upper bound with the best possible constant, unifying and extending some classical inequalities (Hölder, Cauchy–Schwarz, Ostrowski, trapezoidal, and Simpson). We also present explicit constructions demonstrating the sharpness of these inequalities. Furthermore, we explore applications to special functions including the gamma, beta, and modified Bessel functions, highlighting improved bounds and error estimates in numerical integration formulas. The proposed approach extends classical results without requiring strong convexity or boundedness assumptions on derivatives, thereby offering greater flexibility and applicability in both theoretical and applied analysis.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8417191

DOI: 10.1155/jom/8417191

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