Weaker hypotheses for the general projection algorithm with corrections

In an earlier paper [J. of Appl. Math. and Informatics, 29(3-4)(2011), 697-712] we proposed a general projection-type algorithm with corrections and proved its convergence under a set of special assumptions. In this paper we prove convergence of this algorithm under a much weaker set of assumptions. This new framework gives us the possibility to obtain as a particular case of our method the two-step algorithm analysed in [B I T, 38(2)(1998), 275-282].