Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Iva Franjic

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

ifranjic@pbf.hr

Keywords

  • General closed four-point quadrature formula
  • error
  • 4-convex functions
  • Schur-convexity

Mathematics Subject Classification

65D30, 65D32; 26B25

Suggested citation

I. Franjic. “Schur-Convexity of a General Closed Four-Point Quadrature Formula.” Journal of Convex Analysis 25 (2018), No. 3, 767–780.

Copyright Heldermann Verlag 2018