Some Generalized Error Inequalities and Applications.

The article investigates some generalized error inequalities for different classes of function and applications. Researchers have presented a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson's 3/8, and Lobatto four-point quadrature rule for twice-differentiable mapping. Corresponding optimal quadrature formula was found to present better estimate in the context of four-point quadrature formulae of closed type. The study is carried out by using Peano kernel approach in terms of variety of norms, from an inequality point of view.