On Weighted Simpson’s 38 Rule
2021; Multidisciplinary Digital Publishing Institute; Volume: 13; Issue: 10 Linguagem: Inglês
10.3390/sym13101933
ISSN2073-8994
AutoresM. Rostamian Delavar, Artion Kashuri, Manuel De la Sen,
Tópico(s)Iterative Methods for Nonlinear Equations
ResumoNumerical approximations of definite integrals and related error estimations can be made using Simpson’s rules (inequalities). There are two well-known rules: Simpson’s 13 rule or Simpson’s quadrature formula and Simpson’s 38 rule or Simpson’s second formula. The aim of the present paper is to extend several inequalities that hold for Simpson’s 13 rule to Simpson’s 38 rule. More precisely, we prove a weighted version of Simpson’s second type inequality and some Simpson’s second type inequalities for Lipschitzian, bounded variations, convex functions and the functions that belong to Lq. Some applications of the second type Simpson’s inequalities relate to approximations of special means and Simpson’s 38 formula, and moments of random variables are made.
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