Summary: It is proved that a recent theorem of Liu Qihou
[Nonlinear Anal., Theory Methods Appl. 26, No. 11, 1835-1842 (1996; Zbl 0861.47047
)] concerning the iterative approximation of fixed points of demicontractive mappings in Hilbert spaces can be extended to the much more general
-uniformly smooth Banach spaces,
, and to a more general iteration method.