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Journal of Convex Analysis 25 (2018), No. 3, 767--780
Copyright Heldermann Verlag 2018

Schur-Convexity of a General Closed Four-Point Quadrature Formula

Iva Franjic
Faculty of Food- and Bio-Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia

The Schur-convexity property of a general closed four-point quadrature formula is studied and necessary and sufficient conditions for this type of quadrature formula to have this property are given. If a quadrature formula is Schur-convex, this implies the following: if one considers two intervals which share the same midpoint, the error of a Schur-convex quadrature formula is always smaller on a smaller interval.

Keywords: General closed four-point quadrature formula, error, 4-convex functions, Schur-convexity.

MSC: 65D30, 65D32; 26B25

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