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

Iva Franjić

doi:10.68381/jca25053

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 Franjić

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

References

I. Franjić, J. Pečarić, I. Perić: General closed 4-point quadrature formulae of Euler type, Math. Inequal. Appl. 12 (2009) 573–-586.https://doi.org/10.7153/mia-12-45 Google Scholar
F. B. Hildebrand: Introduction to Numerical Analysis, McGraw-Hill Book Company, New York (1956).Google Scholar
V. I. Krylov: Approximate Calculation of Integrals, Macmillan, New York-London (1962).Google Scholar
A. W. Marshall, I. Olkin: Inequalities: Theory of Majorization and Its Applications, Academic Press, New York (1979).Google Scholar
J. E. Pečarić, F. Proschan, Y. L. Tong: Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, New York (1992).Google Scholar

Suggested citation

Published by Heldermann Verlag, 2018. Rights now held by Banach Press LLC.

[1] I. Franjić, J. Pečarić, I. Perić: General closed 4-point quadrature formulae of Euler type, Math. Inequal. Appl. 12 (2009) 573–-586.https://doi.org/10.7153/mia-12-45 Google Scholar

[2] F. B. Hildebrand: Introduction to Numerical Analysis, McGraw-Hill Book Company, New York (1956).Google Scholar

[3] V. I. Krylov: Approximate Calculation of Integrals, Macmillan, New York-London (1962).Google Scholar

[4] A. W. Marshall, I. Olkin: Inequalities: Theory of Majorization and Its Applications, Academic Press, New York (1979).Google Scholar

[5] J. E. Pečarić, F. Proschan, Y. L. Tong: Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, New York (1992).Google Scholar