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Abstract: Numerical integration formulas in n-dimensional Euclidean space of degree three are discussed. In this paper, for the product regions a method is presented to construct numerical integration formulas of degree three with 2n real points and positive weights. The presented problem is a little different from those dealt with by other authors. All the corresponding one-dimensional integrals can be different from each other and they are also nonsymmetrical. In this paper an n-dimensional numerical integration problem is turned into n one-dimensional moment problems, which simplifies the construction process. Some explicit numerical formulas are given. Furthermore, a more generalized numerical integration problem is considered, which will shed light on the final solution to the third degree numerical integration problem. [Copyright &y& Elsevier]

An interesting connection exists between convex functions and uniformly continuous functions. This linkage leads to some interesting functional inequalities over the open interval which works well in quadrature rules and means. In this paper, we establish two new theorem which connect the Hermite–Hadamard type functions. [Copyright &y& Elsevier]