Approximation methods by regular functions (Q2504881)

This is a survey on approximation by smooth functions in Banach spaces. The topics covered by the author, which are at the same time the headings of the sections, are: Approximation by polynomials; Smooth approximation; Analytic approximation; Smooth approximation of norms; Regularization by infimal convolution. The paper includes both classical results (R. Bonic and Frampton, J. Eeells, J. Kurzweil, N. Moulis, J. Mujica, L. Nachbin, H. Torunczyk, H. Whitney, D. Wulbert) as well as some recent ones (D. Azagra, R.M. Aron, M. Cepedello-Boiso, R. Deville, V. Fonf, P. Hájek, R. Haydon, J. G. Llavona, J. B. Prolla, S. Troyanski). No proofs are given. Some open problems are discussed.