INTERPOLATION AND APPROXIMATION FROM CONVEX-SETS

Let X be a topological vector space, Y = R-n, n is an element of N, A be a continuous linear map from X to Y. C subset of X, B be a convex s et dense in C, and d is an element of Y be a data point. We derive con ditions which guarantee that the set B boolean AND A(-1)(d) is nonempt y and dense in C boolean AND A(-1)(d). Some applications to shape pres erving interpolation and approximation are described. (C) 1998 Academi c Press.