An extension of best L2 local approximation

Abstract

We introduce two classes of functions, one containing the classof L2 differentiable functions, and another containing the class of L2 lateraldifferentiable functions. For functions in these new classes we prove existenceof best local approximation at several points. Moreover, we get results aboutthe asymptotic behavior of the derivatives of the net of best approximations,which are unknown even for L2 differentiable functions.