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Schur-convexity and monotonicity of error of a general three-point quadrature formula

We study a general three-point quadrature formula and give necessary and sufficient conditions for this type of quadrature formula to be Schur-convex. A quadrature formula being Schur-convex implies the following: if we consider 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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