Convergence theorems for finite families of Φ-strongly pseudocontractive mappings

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 Φ -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 Φ -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.