Skip to main content

An Iterative Method for a Class of Generalized Global Dynamical System Involving Fuzzy Mappings in Hilbert Spaces

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7666)

Abstract

This paper presents a class of generalized global dynamical system involving (H,η) set-valued monotone mappings and a set-valued function induced by a closed fuzzy mapping in Hilbert spaces. By using the resolvent operator technique and Nadler fixed-point theorem, we prove the equilibrium point set is not empty and closed. Furthermore, we develop a new iterative scheme which generates a Cauchy sequence strongly converging to an equilibrium point.

Keywords

  • Generalized dynamical system
  • Variational inequality
  • equilibrium
  • Fuzzy mapping
  • Iterative method
  • Resolvent operator

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dupuis, P., Nagurney, A.: Dynamical Systems and Variational Inequalities. Ann. Oper. Res. 44, 19–42 (1993)

    CrossRef  MathSciNet  Google Scholar 

  2. Friesz, T.L., Bernstein, D.H., Mehta, N.J., Tobin, R.L., Ganjlizadeh, S.: Day-to-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems. Oper. Res. 42, 1120–1136 (1994)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Xia, Y.S., Vincent, T.L.: On the Stability of Global Projected Dynamical Systems. J. Optim. Theory Appl. 106, 129–150 (2000)

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Zhang, D., Nagurney, A.: On the Stability of Projected Dynamical Systems. J. Optim. Theory Appl. 85, 97–124 (1995)

    CrossRef  MathSciNet  Google Scholar 

  5. Zou, Y.Z., Huang, N.J., Lee, B.S.: A New Class of Generalized Global Set-Valued Dynamical Systems Involving \(\left( H,\eta \right) \) -monotone operators in Hilbert Spaces. Nonlinear Analysis Forum 12(2), 191–193 (2007)

    MathSciNet  Google Scholar 

  6. Zadeh, L.A.: Fuzzy Sets. Inform. Control 8, 338–353 (1965)

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Zou, Y., Huang, N.: An Iterative Method for Quasi-Variational-Like Inclusions with Fuzzy Mappings. In: Wang, G.-Y., Peters, J.F., Skowron, A., Yao, Y. (eds.) RSKT 2006. LNCS (LNAI), vol. 4062, pp. 349–356. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  8. Fang, Y.P., Huang, N.J., Tompson, H.B.: A New System of Variational Inclusions with (H,η)-Monotone Operators in Hilbert Spaces. Comput. Math. Appl. 49(2-3), 365–374 (2005)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Nadler, S.B.: Multivalued Contraction Mappings. Pacific J. Math. 30, 475–485 (1969)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zou, Yz., Wu, Xk., Zhang, Wb., Sun, Cy. (2012). An Iterative Method for a Class of Generalized Global Dynamical System Involving Fuzzy Mappings in Hilbert Spaces. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34478-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34478-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34477-0

  • Online ISBN: 978-3-642-34478-7

  • eBook Packages: Computer ScienceComputer Science (R0)