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Schur-Convexity and Monotonicity of Error of a General Three-Point Quadrature Formula

A general three-point quadrature formula is studied and necessary and sufficient conditions for this type of quadrature formula to be Schur-convex are given. A quadrature formula being Schur-convex implies the following: if one considers two intervals, one of which contains the other, and such that share the same midpoint, then the error of this quadrature formula is smaller on a smaller interval.

Schur-convexity; general three-point quadrature formula; 4-convex functions; Bernoulli polynomials

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