Abstract
In this work, we first establish a general Marsden’s identity for Unified and Extended B-splines (UE B-splines or Omega B-splines for short). Then, by using this result, we construct univariate omega spline quasi-interpolants on a bounded interval and we study their approximation errors. For particular values of omega, we refind some already developed quasi-interpolants. As a practical side of these operators, we give some applications to numerical analysis especially quadrature formulas, differentiation and numerical solutions of linear Fredholm integral equations, which are illustrated by some numerical examples.
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