In this note, an open question proposed by Marek and Szyld is solved (I. Ma
rek, D.B. Szyld, Comparison theorems for weak splittings of bounded operato
rs, Numer. Math. 58 (1990) 387-397). At the same time, some new comparison
theorems are presented. (C) 2000 Elsevier Science Inc. All rights reserved.