Convergence theorems for finite families of $$\Phi $$ Φ -strongly pseudocontractive mappings

Abstract

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 $$\Phi $$ -pseudocontractive mapping $$T:K\rightarrow K$$ under certain conditions then such an iterative process can be used to approximate the unique common fixed point of a finite family of $$\Phi $$ -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.