Skip to main content
SpringerLink
Log in

On the convergence problems of Ishikawa and Mann iterative processes with error for Φ-pseudo contractive type mappings

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The purpose of this paper is to introduce the concept of Φ-pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors' recent results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dunn J C. Iterative construction of fixed points for multivalued operators of the monotone type[J].J. Functi Anal, 1978,27, 38–50.

    Article  MATH  MathSciNet  Google Scholar 

  2. Chidume C E. Iterative construction of fixed points for multivalued operators of the monotone type [J].Appl Anal, 1996,23:209–218.

    MathSciNet  Google Scholar 

  3. Chang S S, Tan K K. Iteration processes of fixed point for operators of monotone type in Banach spaces[J].Bull Austral Math Soc, 1998,57: 433–445.

    Article  MATH  MathSciNet  Google Scholar 

  4. Osilike M O. Iterative solution of nonlinear equations of the ϕ-strongly accretive strongly accretive type[J].J Math Anal Appl, 1996,200:259–271.

    Article  MATH  MathSciNet  Google Scholar 

  5. Browder F E. Nonlinear mappings of nonexpansive and accretive type in Banach spaces [J].Bull Amer Math Soc, 1967,73: 875–882.

    Article  MATH  MathSciNet  Google Scholar 

  6. Kato T. Nonlinear semi-groups and evolution equations[J].J Math Soc Japan, 1964,19:508–520.

    Article  Google Scholar 

  7. Ishikawa S. Fixed point by a new iteration method[J].Proc Amer Math Soc, 1974,14(1):147–150.

    Article  MathSciNet  Google Scholar 

  8. Mann W R. Mean value methods in iteration[J].Proc Amer Math Soc, 1953,4:506–510.

    Article  MATH  MathSciNet  Google Scholar 

  9. Chang S S. On Chidume's open questions and approximate solutions of multivalued strongly accretive mappings equations in Banach spaces[J].J Math Anal Appl, 1997,216:94–111.

    Article  MATH  MathSciNet  Google Scholar 

  10. Chang S S. Some problems and results in the study of nonlinear analysis [J].Nonlinear Anal, 1997,30(7):4197–4208.

    Article  MATH  MathSciNet  Google Scholar 

  11. Chidume C E. Approximation of fixed points of strongly pseudo-contractive mappings[J].Proc Amer Math Soc, 1994,120(2): 545–551.

    Article  MATH  MathSciNet  Google Scholar 

  12. Chidume C E. Steepest descent approximations for accretive operator equations[J].Nonlinear Anal, 1996,26:299–311.

    Article  MATH  MathSciNet  Google Scholar 

  13. Chidume C E. Iterative solution of nonlinear equations with strongly accretive operators[J].J Math Anal Appl, 1995,192:502–518.

    Article  MATH  MathSciNet  Google Scholar 

  14. Chidume C E, Osilike M O. Ishikawa process for nonlinear Lipschitz strongly accretive mappings [J].J Math Anal Appl, 1995,192:727–741.

    Article  MATH  MathSciNet  Google Scholar 

  15. Deng Lei. On Chidume's open questions[J].J Math Anal Appl, 1993,174(2):441–449.

    Article  MATH  MathSciNet  Google Scholar 

  16. Deng Lei, Ding Xieping. Iterative approximation of Lipschitz strongly pseudo-contractive mappings in uniformly smooth Banach spaces[J].Nonlinear Anal, 1995,24:981–987.

    Article  MATH  MathSciNet  Google Scholar 

  17. Osilike M O. Stable iteration procedures of strong pseudo-contractions and nonlinear operator equations of the accretive type[J].J Math Anal Appl, 1996,204:677–692.

    Article  MATH  MathSciNet  Google Scholar 

  18. Osilike M O. Iterative construction of fixed points of multi-valued operators of the accretive type [J].Soochow J Math, 1996,22(4):485–494.

    MATH  MathSciNet  Google Scholar 

  19. Reich S. An iterative procedure for constructing zeros of accretive sets in Banach spaces [J].Nonlinear Anal, 1978,2:85–92.

    Article  MATH  MathSciNet  Google Scholar 

  20. Reich S. Strong convergence theorems for resolvents of accretive operators in Banach spaces[J].Math Anal Appl, 1980,85:287–292.

    Article  Google Scholar 

  21. Tan K K, Xu H K. Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces[J].J Math Anal Appl, 1993,178:9–21.

    Article  MATH  MathSciNet  Google Scholar 

  22. Zhou H Y. Remarks on Ishikawa iteration[J].Chinese Sci Bull, 1977,42:126–128.

    Google Scholar 

  23. Liu L S. Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl, 1995,194:114–125.

    Article  MATH  MathSciNet  Google Scholar 

  24. Zeidler E.Nonlinear Functional Analysis and Its Applications [M]. Part II, Monotone Operators, New York/Berlin: Springer-Verlag, 1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Sichuan University, 610064, Chengdu, P R China

    Zhang Shisheng Professor

Authors
  1. Zhang Shisheng Professor
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Foundation item: the National Natural Science Foundation of China (19971058)

Biography: Zhang Shisheng (1934-)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shisheng, Z. On the convergence problems of Ishikawa and Mann iterative processes with error for Φ-pseudo contractive type mappings. Appl Math Mech 21, 1–12 (2000). https://doi.org/10.1007/BF02458533

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458533

Key words

CLC number

Search

Navigation