On discrete, differentiel and integral spline quasi-interpolants and their applications

In the theory of approximation, the spline quasi-interpolants play a significant role and are used extensively. Several authors have proposed various methods over the past few years for approximating the solution of various classes of functional equations using spline quasi-interpolants. The numerical solution of integral equations with a smooth kernel utilizing collocation and projection methods with discrete spline quasi-interpolants has received a lot of attention lately. The development of the differential and integral spline quasi-interpolants as well as an attempt to provide novel structures for these spline quasi-interpolants are the two main goals of this thesis. On the other hand, we will apply our findings to the solution of a few groups of functional equations.