Skip to main content
SpringerLink
Log in

A-Monotonicity and Its Role in Nonlinear Variational Inclusions

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

Abstract

The notion of A-monotonicity in the context of solving a new class of nonlinear variational inclusion problems is presented. Since A-monotonicity generalizes not only the well-explored maximal monotone mapping, but also a recently introduced and studied notion of H-monotone mapping, the results thus obtained are general in nature.

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., and Huang, N. J., Sensitivity Analysis for Strongly Nonlinear Quasivariational Inclusions, Applied Mathematics Letters, Vol. 13, No. 1, pp. 19–24, 2000.

    Article  MathSciNet  Google Scholar 

  2. Tobin, R. L., Sensitivity Analysis for Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 48, No. 1, pp. 191–204, 1986.

    MathSciNet  Google Scholar 

  3. Fang, Y. P., and Huang, N. J., H-Monotone Operator and Resolvent Operator Technique for Variational Inclusions, Applied Mathematics and Computation, Vol. 145, No. 2, pp. 795–803, 2003.

    Article  MathSciNet  Google Scholar 

  4. Fang, Y. P., and Huang, N. J., H-Monotone Operators and System of Variational Inclusions, Communications on Applied Nonlinear Analysis, Vol. 11, No. 1, pp. 93–101, 2004.

    MathSciNet  Google Scholar 

  5. Liu, Z., Ume, J. S., and Kang, S. M., H-Monotone Operator and Resolvent Operator Technique for Nonlinear Variational Inclusions, Mathematical Inequalities and Applications (to appear).

  6. Verma, R. U., A-Monotonicity and Applications to Nonlinear Variational Inclusion Problems, Journal of Applied Mathematics and Stochastic Analysis, Vol. 17, No. 2, pp. 193–195, 2004.

    Article  Google Scholar 

  7. Verma, R. U., Approximation-Solvability of a Class of A-Monotone Variational Inclusion Problems, Journal of the Korea Society for Industrial and Applied Mathematics, Vol. 8, No. 1, pp. 55–66, 2004.

    Google Scholar 

  8. Ding, X. P., and Luo, C. L., On Parametric Generalized Quasi-Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 100, No. 1, pp. 195–205, 1999.

    Article  MathSciNet  Google Scholar 

  9. Huang, N. J., and Fang, Y. P., Auxiliary Principle Technique for Solving Generalized Set-Valued Nonlinear Quasivariational-Like Inequalities, Mathematical Inequalities and Applications (to appear).

  10. Iiduka, H., and Takahashi, W., Strong Convergence Theorem by a Hybrid Method for Nonlinear Mappings of Nonexpansive and Monotone Type and Applications, Advances in Nonlinear Variational Inequalities, Vol. 9, No. 1, pp. 1–9, 2006.

    MathSciNet  Google Scholar 

  11. Kyparisis, J., Sensitivity Analysis Framework for Variational Inequalities, Mathematical Programming, Vol. 38, No. 1, pp. 203–213, 1987.

    MathSciNet  Google Scholar 

  12. Moudafi, A., Mixed Equilibrium Problems: Sensitivity Analysis and Algorithmic Aspect, Computers and Mathematics with Applications, Vol. 44, No. 9, pp. 1099–1108, 2002.

    Article  MathSciNet  Google Scholar 

  13. Verma, R. U., Nonlinear Variational and Constrained Hemivariational Inequalities Involving Relaxed Operators, ZAMM: Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 77, No. 5, pp. 387–391, 1997.

    Google Scholar 

  14. Verma, R. U., Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods, Journal of Optimization Theory and Applications, Vol. 121, No. 1, pp. 203–210, 2004.

    Article  MathSciNet  Google Scholar 

  15. Verma, R. U., Generalized Partial Relaxed Monotonicity and Non-linear Variational Inequalities, Journal of Applied Mathematics, Vol. 9, No. 4, pp. 355–363, 2002.

    MathSciNet  Google Scholar 

  16. Yan, W. Y., Fang, Y. P., and Huang, N. J., A New System of Set-Valued Variational Inclusions with H-Monotone Operators, Mathematical Inequalities and Applications (to appear).

  17. Zeidler, E., Nonlinear Functional Analysis and Its Applications, Vol. II/A, Springer-Verlag, New York, NY, 1985.

    Google Scholar 

  18. Zeidler, E., Nonlinear Functional Analysis and Its Applications, Vol. II/B, Springer-Verlag, New York, NY, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Applied Mathematics, University of Akron, Akron, Ohio, USA

    R. U. Verma (Senior Lecturer)

Authors
  1. R. U. Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Leitmann

Rights and permissions

Reprints and permissions

About this article

Cite this article

Verma, R.U. A-Monotonicity and Its Role in Nonlinear Variational Inclusions. J Optim Theory Appl 129, 457–467 (2006). https://doi.org/10.1007/s10957-006-9079-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-006-9079-7

Keywords

Search

Navigation