This research paper deals with the splines induced by an original method which generates, in particular, the best simultaneous (vectorial) approximation and optimal interpolation elements in any H-locally convex space, that is, in every Hausdorff locally convex space with each semi-norm satisfying the parallelogram law, applied to a class of set functions. In such a way as this, we indicate again our first procedure which extends, in a natural manner, the Best Approximation Problem solved by the usual spline functions in Hilbert spaces to the H-locally convex spaces.