The problem of image recovery by the metric projections in Banach spaces (Q1949517)

Summary: We consider the problem of image recovery by the metric projections in a real Banach space. For a countable family of nonempty closed convex subsets, we generate an iterative sequence converging weakly to a point in the intersection of these subsets. Our convergence theorems extend the results proved by \textit{L. M. Bregman} [Sov. Math., Dokl. 6, 688--692 (1965); translation from Dokl. Akad. Nauk SSSR 162, 487--490 (1965; Zbl 0142.16804)] and \textit{G. Crombez} [J. Math. Anal. Appl. 155, No.~2, 413--419 (1991; Zbl 0752.65045)].