Error Estimation of Weddle’s Rule for Generalized Convex Functions with Applications to Numerical Integration and Computational Analysis

Abdul Mateen (), Bandar Bin-Mohsin (), Ghulam Hussain Tipu and Asia Shehzadi
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Abdul Mateen: Ministry of Education Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Bandar Bin-Mohsin: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Ghulam Hussain Tipu: Department of Mathematics, Shanghai University and Newtouch Center for Mathematics of Shanghai University, Shanghai 200444, China
Asia Shehzadi: School of Mathematics and Statistics, Central South University, Changsha 410083, China

Mathematics, 2025, vol. 13, issue 17, 1-18

Abstract: This paper presents new integral inequalities for differentiable generalized convex functions in the second sense, with a focus on improving the accuracy of Weddle’s formula for numerical integration. The study is motivated by the following three key factors: the generalization of convexity through s -convex functions, the enhancement of the approximation quality, particularly as s → 0 + , and the effectiveness of Weddle’s formula in cases where Simpson’s 1/3 rule fails. An integral identity is derived for differentiable functions, which is then used to establish sharp error bounds for Weddle’s formula under s -convexity. Numerical examples and comparative tables demonstrate that the proposed inequalities yield significantly tighter bounds than those based on classical convexity. Applications to numerical quadrature highlight the practical utility of the results in computational mathematics.

Keywords: Weddle formula-type inequality; quadrature formulas; error bounds; convex functions; s -convex function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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