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Afrika Matematika

, Volume 29, Issue 3–4, pp 399–406 | Cite as

Convergence theorems for finite families of \(\Phi \)-strongly pseudocontractive mappings

  • Ahmed A. Abdelhakim
  • R. A. Rashwan
Article
  • 43 Downloads

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.

Keywords

Common fixed point Iterative approximation \(\Phi \)-pseudocontractive 

Mathematics Subject Classification

47H06 47H09 47J05 47J25 

References

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceAssiut UniversityAssiutEgypt

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