Quasi-interpolations with interpolation property. (Q1427247)

Let \(\Omega \subset \mathbb R^s\) and \(B(\Omega)\) be the set consisting in all bounded functions over \(\Omega\). Let \(T:B(\Omega) \to B(\Omega)\) be a linear operator and \(X=\{ x_1,\ldots,x_r \}\) a set of points. \(T\) is called a linear operator with interpolation property (A) if \((Tf)(x_j)=f(x_j)\) for any \(f \in B(\Omega)\) and \(j=1,\ldots,r\). An operator \(V:B(\Omega) \to B(\Omega)\) is called quasi-interpolation operator if \(Vf=f\) for all polynomials of degree at most \(n\). In this paper the authors present a method, using an interpolation operator and a quasi-interpolation operator, to construct a quasi-interpolation operator with interpolation property (A).