Skip to main content
SpringerLink
Log in

Some results of variational inclusion problems and fixed point problems with applications

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

Abstract

This paper introduces a general iterative algorithm to approximate a common element in the solution set of quasi-variational inclusion problems and the common fixed point set of an infinite family of nonexpansive mappings. It is proven that the iterative sequences generated in the proposed iterative algorithm converge strongly to some common element in the framework of the real Hilbert spaces.

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. Chang, S. S. Set-valued variational inclusions in Banach spaces. J. Math. Anal. Appl. 248(2), 438–454 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Noor, M. A. and Noor, K. I. Sensitivity analysis for quasi-variational inclusions. J. Math. Anal. Appl. 236(2), 290–299 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Zhang, S. S., Lee, J. H. W., and Chan, C. K. Algorithms of common solutions to quasi variational inclusion and fixed point problems. Appl. Math. Mech. -Engl. Ed. 29(5), 571–581 (2008) DOI: 10.1007/s10483-008-0502-y

    Article  MATH  MathSciNet  Google Scholar 

  4. Chang, S. S., Lee, H. W. J., and Chan, C. K. A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization. Nonlinear Analysis 70(9), 3307–3319 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Qin, X. L., Shang, M. J., and Su, Y. F. Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems. Mathematical and Computer Modelling 48(7–8), 1033–1046 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Xu, H. K. An iterative approach to quadratic optimization. J. Optim. Theory Appl. 116(3), 659–678 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Shimoji, K. and Takahashi, W. Strong convergence to common fixed points of infinite nonexpansive mappings and applications. Taiwanese J. Math. 5(2), 387–404 (2001)

    MATH  MathSciNet  Google Scholar 

  8. Suzuki, T. Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals. J. Math. Anal. Appl. 305(1), 227–239 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pascali, D. and Sburlan, S. Nonlinear Mappings of Monotone Type, Sijthoff & Noordhoff International Publishers, The Netherlands (1978)

    MATH  Google Scholar 

  10. Opial, Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Amer. Math. Soc. 73(4), 595–597 (1967)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316004, Zhejiang Province, P. R. China

    Yan Hao  (郝彦)

  2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, Zhejiang Province, P. R. China

    Yan Hao  (郝彦)

Authors
  1. Yan Hao  (郝彦)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Hao  (郝彦).

Additional information

Communicated by Xie-ping DING

Project supported by the National Natural Science Foundation of China (No. 10901140)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hao, Y. Some results of variational inclusion problems and fixed point problems with applications. Appl. Math. Mech.-Engl. Ed. 30, 1589–1596 (2009). https://doi.org/10.1007/s10483-009-1210-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-009-1210-x

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation