New Simpson Type Quadrature Formulas for Any Order Differentiable Functions Simpson Type Quadrature Rules
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Keywords:
Bounded Function, Differentiable Function, Simpson's Rules, Error Estimation, Numerical IntegrationAbstract
This paper is devoted to establishing error estimates for the Simpson-type quadrature formula in
the case of functions whose higher-order derivatives are either bounded or belong to the Lp space. Initially,
the fundamental inequalities introduced by Erden et al. in [7] are stated. Subsequently, the Simpson-type
quadrature rules obtained by means of these inequalities are examined for the mentioned classes of
functions. In addition, the relationships between the particular cases of the derived quadrature formulas and
the existing formulas reported in the literature were analyzed.
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References
Alomari, M., Darus, M., & Dragomir, S.S. (2009). New inequalities of Simpson's type for s-convex functions with applications. Research Report Collection, 12(4).
Anastassiou, G. (1995). Ostrowski type inequalities. Proceeding of the American Mathematical. Society, 123 (12), 3775-378
Dragomir, S.S., Agarwal, R.P., & Cerone, P. (2000). On Simpson's inequality and applications. RGMIA Research Report Collection, 2(3). J. of Inequal. Appl., 5, 533-579.
Erden, S., & Başkir, M.B. (2021). Improved results on perturbed inequalities for higher-order differentiable functions and their various applications. Filomat, 35(10), 3475-3490.
Erden, S., Celik, N., & Khan, M. A. (2021). Refined inequalities of perturbed Ostrowski type for higher-order absolutely continuous functions and applications. AIMS Mathematics, 6(1), 362-377.
Erden, S., Iftikhar, S., Kumam, P., and Thounthong, P. (2024). On error estimations of Simpson's second type quadrature formula. Mathematical Methods in the Applied Sciences, 47(13), 11232-11244.
Erden, S., Demir, C., and Alkan, S. (2025). Refined Inequalities of Perturbed Simpsons Type for Higher-Order Absolutely Continuous Functions and Applications, Submited.
Fink, M.A. Bounds on the deviation of a function from its averages, Czechoslovak Mathematical Journal, 42 (1992), 117, pp. 289-310.
Liu, Z. (2005). An inequality of Simpson type. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2059), 2155-2158.
Liu, W., Wang, Y., Sial, I. B., & Ciurdariu, L. (2025). Some New and Sharp Inequalities of Composite Simpson's Formula for Differentiable Functions with Applications. Mathematics, 13(11), 1814.
Qayyum, A., Kashif, A. R., Shoaib, M., & Faye, I. (2016). Derivation of New Efficient Quadrature Rules Using Ostrowski Type Integral Inequalities for n- Times Differentiable Mappings. J Inequal Special Funct, 7(3).
Qayyum, A., Shoaib, M., & Faye, I. (2017). On new refinements and applications of efficient quadrature rules using n-times differentiable mappings. J. Comput. Anal. Appl, 23(4), 723-739.
Sarikaya, M.Z., & Bardak, S. (2019). Generalized Simpson type integral inequalities. Konuralp Journal of Mathematics, 7(1), 186-191.
