On Some Classes of Interpolating Splines

In this article, we consider some classes of interpolating spline with difference. derivative and integral interpolating conditions respectively. Let Δ:a=x<u<v≤X≤U<v≤X…X≤U,<v≤xbe a partition of [a, b], where and suppose （x） be a function defined on [a, b] and （x）∈C[a,b]. In the first place, we consider cubic interpolating splines s（x） and s（x） satisfying the following conditions respectively: （i） s（x） (s（x）)∈C[a, b]; （ii） s（x） (s（x）) is cubic polynomial in each interval [x, x]; （ⅲ） s（v）-s（u）=（v）