Improved error limits for numerical integration via some perturbed trapezoidal inequalities.

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Bibliographic Details
Title:	Improved error limits for numerical integration via some perturbed trapezoidal inequalities.
Authors:	DÖNMEZ DEMİR, Duygu¹ duygu.donmez@cbu.edu.tr, ŞANAL, Gülsüm²
Source:	Sigma: Journal of Engineering & Natural Sciences / Mühendislik ve Fen Bilimleri Dergisi. Feb2026, Vol. 44 Issue 1, p309-317. 9p.
Subjects:	Numerical integration, Integral inequalities, Approximation error, Mathematical optimization, Convex functions
Abstract:	Integral inequalities prove extremely effective in obtaining error bounds for numerical integration formulas, which are particularly useful in optimization problems. This study presents reduced results of perturbed trapezoidal inequalities derived using the triangle inequality, Hölder’s inequality, and power mean inequalities for previously constructed nth-order differentiable s-convex and tgs-convex functions. These results help determine error limits for the trapezoidal rule and the remaining term of the midpoint formula in numerical integration. The study shows that these reduced inequalities yield better error limits. Additionally, an example involving a tgs-convex function defined under certain conditions demonstrates the practical application of these theoretical results. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	Integral inequalities prove extremely effective in obtaining error bounds for numerical integration formulas, which are particularly useful in optimization problems. This study presents reduced results of perturbed trapezoidal inequalities derived using the triangle inequality, Hölder’s inequality, and power mean inequalities for previously constructed nth-order differentiable s-convex and tgs-convex functions. These results help determine error limits for the trapezoidal rule and the remaining term of the midpoint formula in numerical integration. The study shows that these reduced inequalities yield better error limits. Additionally, an example involving a tgs-convex function defined under certain conditions demonstrates the practical application of these theoretical results. [ABSTRACT FROM AUTHOR]
ISSN:	13047191
DOI:	10.14744/sigma.2026.1983