Skip to main content
SpringerLink
Log in

A New Class of Monotone Mappings and a New Class of Variational Inclusions in Banach Spaces

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, we introduce and study a new class of variational inclusions in Banach spaces. As it concerns the methods of solution, we introduce a new class of monotone mappings. We define a proximal mapping associated with this mappings and show its Lipschitz continuity. By using the technique of proximal mapping, we construct a new iterative algorithm. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. Our results improve and generalize many known 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. Agarwal, R.P., Cho, Y.J., Huang, N.J.: Sensivity analysis for strongly nonlinear quasi-variational inclusions. J. Appl. Math. Lett. 13(16), 19–24 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahmad, R., Ansari, Q.H.: An iterative algorithm for generalized nonlinear variational inclusions. J. Appl. Math. Comput. 145, 795–803 (2003)

    Google Scholar 

  4. Xia, F.Q., Huang, N.J.: Variational inclusions with a general H-monotone operator in Banach spaces. J. Comput. Math. Appl. 54, 24–30 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Luo, X.P., Huang, N.J.: A new class of variational inclusions with B-monotone operators in Banach spaces. J. Comput. Appl. Math. 233, 1888–1896 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Feng, H.R., Ding, X.P.: A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces. J. Comput. Appl. Math. 225, 365–373 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pertryshyn, W.V.: A characterization of strictly convexity of Banach spaces and other uses of duality mappings. J. Funct. Anal. 6, 282–291 (1970)

    Article  Google Scholar 

  8. Ding, X.P., Feng, H.R.: Algorithm for solving a new class of generalized nonlinear implicit quasi-variational inclusions in Banach spaces. J. Appl. Math. Comput. 208, 547–555 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Fang, Y.P., Huang, N.J.: H-monotone and resolvent operator technique for variational inclusions. J. Appl. Math. Comput. 145, 795–803 (2003)

    MathSciNet  MATH  Google Scholar 

  10. Xia, F.Q., Huang, N.J.: Algorithm for solving a new class of general mixed variational inequalities in Banach spaces. J. Comput. Appl. Math. 220, 632–642 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Yasouj University, Yasouj, 75914, Iran

    Sayyedeh Zahra Nazemi

Authors
  1. Sayyedeh Zahra Nazemi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sayyedeh Zahra Nazemi.

Additional information

Communicated by Byung-Soo Lee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nazemi, S.Z. A New Class of Monotone Mappings and a New Class of Variational Inclusions in Banach Spaces. J Optim Theory Appl 155, 785–795 (2012). https://doi.org/10.1007/s10957-012-0096-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-012-0096-4

Keywords

Search

Navigation