On a functional equation connected to Gauss quadrature rule

Barbara Koclęga-Kulpa; Tomasz Szostok

Published: 2008-09-30

Vol. 22 (2008)

On a functional equation connected to Gauss quadrature rule

Barbara Koclęga-Kulpa , Tomasz Szostok

Abstract

We consider the functional equation
F(y)−F(x) = (y−x)[f(αx+βy)+f(βx+αy)]
stemming from Gauss quadrature rule. In previous results equations of this type with rational only coefficients α and β were considered. In this paper we allow these numbers to be irrational. We find all solutions of this equation for functions acting on ℝ. However, some results are valid also on integral domains.

Keywords:

functional equations on integral domains , quadrature rules

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Koclęga-Kulpa, B., & Szostok, T. (2008). On a functional equation connected to Gauss quadrature rule. Annales Mathematicae Silesianae, 22, 27–40. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14049

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Barbara Koclęga-Kulpa

Affiliation:

Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland

Tomasz Szostok

szostok@math.us.edu.pl

Affiliation:

Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland

Vol. 22 (2008)
Published: 2008-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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