Convergence of string-averaging projection schemes for inconsistent convex feasibility problems

We study iterative projection algorithms for the convex feasibility problem of Þnding a point in the intersection of Þnitely many nonempty, closed and convex subsets in the Euclidean space. We propose (without proof) an algorithmic scheme which generalizes both the stringaveraging algorithm and the block-iterative projections (BIP) method with Þxed blocks and prove convergence of the string-averaging method in the inconsistent case by translating it into a fully sequential algorithm in the product space.