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On Functional Equations Connected with Quadrature Rules
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Barbara Koclęga-Kulpa
Veröffentlicht/Copyright:
11. März 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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- On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems
- Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations
- Unilateral Contact Problems with Friction for Hemitropic Elastic Solids
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- The Jawerth–Franke Embedding of Spaces with Dominating Mixed Smoothness
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- 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
- On Functional Equations Connected with Quadrature Rules
- 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
- On Solutions of a Singular Viscoelastic Equation with an Integral Condition
- Nonbounding 𝑛-C.E. 𝑄-Degrees
- Nonequivalence of Unilateral Strong Differentiation Bases in
Schlagwörter für diesen Artikel
Approximate integration;
functional equations;
polynomial functions;
quadrature rules
Artikel in diesem Heft
- On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems
- Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations
- Unilateral Contact Problems with Friction for Hemitropic Elastic Solids
- 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
- On Functional Equations Connected with Quadrature Rules
- 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
- On Solutions of a Singular Viscoelastic Equation with an Integral Condition
- Nonbounding 𝑛-C.E. 𝑄-Degrees
- Nonequivalence of Unilateral Strong Differentiation Bases in
