Suppose E is a Banach space with certain geometric properties and K is a
nonempty closed convex subset of E.We prove that if a certain iterative sequence converges
to the unique fixed point of a -pseudocontractive mapping T : K → K under certain
conditions then such an iterative process can be used to approximate the unique common
fixed point of a finite family of -pseudocontractive self mappings of K. Our results extend
and generalize the results in Chidume (Proc Am Math Soc 120:2641–2649, 1994; Proc Am
Math Soc 9:545–551, 1998), Huang (Comput Math Appl 36:13–21, 1998), Liu (Comput
Math Appl 45:623–634, 2003), Osilike (Math Anal Appl 200:259–271, 1996; Nonlinear
Anal 36:1–9, 1999) and many others