Skip to main content
SpringerLink
Log in

Convergence of Iterative Methods for an Infinite Family of Pseudo-contractions

  • Conference paper
Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

  • 1857 Accesses

Abstract

In this paper, we establish some strong convergence theorems for an infinitely countable family of Lipschitzian pseudo-contractions in Hilbert spaces by proposing some kinds of new iterative methods. The results here extend and improve the corresponding results of other authors’, such as Haiyun Zhou [Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces, J Math Anal Appl 343: 546-556 ], Marino G and Xu H K [Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J Math Anal Appl 329(1): 336-346 ], Rhoades B E [Fixed point iterations using infinite matrices, Trans Amer Math Soc 196: 162-176].

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Browder, F.E., Petryshyn, W.V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. Math. Anal. Appl. 20, 197–228 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  2. Mann, W.R.: Mean value methods in iterations. Proc. Amer. Math. Soc. 4, 506–510 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  3. Marino, G., Xu, H.K.: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 329(1), 336–346 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Reich, S.: Asymptotic behavior of contractions in Banach spaces. J. Math. Anal. Appl. 44, 57–70 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  5. Rhoades, B.E.: Fixed point iterations using infinite matrices. Trans. Amer. Math. Soc. 196, 162–176 (1974)

    Article  MathSciNet  Google Scholar 

  6. Wang, Y.H., Zeng, L.C.: Convergence of generalized projective modified iteration methods in Banach spaces. Chinese Ann. Math. Ser. A 30(1), 55–62 (2009) (in Chinese)

    MathSciNet  MATH  Google Scholar 

  7. Zhou, H.Y.: Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 343, 546–556 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhou, H.Y., Su, Y.F.: Strong convergence theorems for a family of quasi-asymptotic pseudo-contractions in Hilbert spaces. Nonlinear Anal. 70(11), 4047–4052 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Yuanheng Wang & Jiashuai Dong

Authors
  1. Yuanheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiashuai Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, Y., Dong, J. (2011). Convergence of Iterative Methods for an Infinite Family of Pseudo-contractions. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22833-9_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation