A sharp estimate for the Peano error representation

作者：Gavrea Ioan^*; Ivan Mircea

来源：Applied Mathematics and Computation, 2015, 252: 14-19.

DOI：10.1016/j.amc.2014.12.017

• Error bounds for quadrature formulas
• Numerical integration
• Peano error representation
• Ostrowski type inequality
• Gruss type inequality
• Linear functionals

We provide a sharp estimate of the Peano error representation formula for linear functionals. As applications, we obtain sharp estimates for the remainder term in general quadrature formulae and expand some Ostrowski-like type inequalities to linear functionals. The new approach extends and unifies many earlier results on the subject (Dragomir and Wang, 1997; Cheng, 2001; Matic, 2003; Vong, 2011; Gonska et al., 2012).

• 出版日期2015-2-1