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On Functional Equations Connected with Quadrature Rules
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Barbara Koclęga-Kulpa
Published/Copyright:
March 11, 2010
Abstract
The functional equations of the form
are considered. They are connected with quadrature rules of the approximate integration. We show that such equations characterize polynomials in the class of continuous functions. It is also shown that if the number of components is sufficiently small, then the continuity is forced by the equation itself. Unique solvability of the considered problem are established.
Key words and phrases:: Approximate integration; functional equations; polynomial functions; quadrature rules
Received: 2008-10-27
Revised: 2009-05-25
Published Online: 2010-03-11
Published in Print: 2009-December
© Heldermann Verlag
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Keywords for this article
Approximate integration;
functional equations;
polynomial functions;
quadrature rules
Articles in the same Issue
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- Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations
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- A Periodic Boundary Value Problem for Functional Differential Equations of Higher Order
- The Jawerth–Franke Embedding of Spaces with Dominating Mixed Smoothness
- Stability by Fixed Point Theory for Nonlinear Delay Difference Equations
- On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their Bézier Variant
- On Nonmeasurable Functions of Two Variables and Iterated Integrals
- Bounded and Vanishing at Infinity Solutions of Nonlinear Differential Systems
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- The Riemann–Hilbert Problem in a Domain with Piecewise Smooth Boundaries in Weight Classes of Cauchy Type Integrals with a Density from Variable Exponent Lebesgue Spaces
- A Counterexample on Embedding of Spaces
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