Afrika Matematika

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

Convergence theorems for finite families of \(\Phi \)-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 \(\Phi \)-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.


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

Mathematics Subject Classification

47H06 47H09 47J05 47J25 


  1. 1.
    Ahmed, A.A., Feng, G.: On solving Lipschitz pseudocontractive operator equations. Inequalities Appl. 2014, 314 (2014)Google Scholar
  2. 2.
    Chidume, C.E.: Approximation of fixed points of strongly pseudocontractive mappings. Proc. Am. Math. Soc. 120, 2641–2649 (1994)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Chidume, C.E.: Global iteration for pseudocontractive maps. Proc. Am. Math. Soc. 9, 545–551 (1998)Google Scholar
  4. 4.
    Huang, Z.: Approximating fixed points of \(\Phi \)-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces. Comput. Math. Appl. 36, 13–21 (1998)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Liu, Zeqing: Iterative solutions of nonlinear equations with \(\Phi \)-strongly accretive operators in uniformly smooth Banach spaces. Comput. Math. Appl. 45, 623–634 (2003)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Osilike, M.O.: Iterative solution of nonlinear equations of the-strongly accretive type. J. Math. Anal. Appl. 200, 259–271 (1996)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Osilike, M.O.: Iterative solutions of nonlinear \(\Phi \)-strongly accretive operator equations in arbitrary Banach spaces. Nonlinear Anal. 36, 1–9 (1999)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Reich, S.: An iterative procedure for constructing zeros of accretive sets in Banach spaces. Nonlinear Anal. 2, 85–92 (1978)MathSciNetCrossRefMATHGoogle Scholar

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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