Construction of univariate spline quasi-interpolants with symmetric functions

A new approach to construct univariate spline quasi-interpolants on arbitrary partitions of bounded intervals is developed. In the first part of this paper, we give some results about the symmetric functions of the difference of two finite sets. These results are used, in the second part of this work, to construct explicitly different types of quasi-interpolants. We revise the definition of a uniformly bounded quasi-interpolant and we propose some results on this subject. Some numerical examples are given to illustrate our theoretical results.