Nothing Special   »   [go: up one dir, main page]
Skip to main content

Advertisement

Springer Nature Link
Log in

Iterative schemes for trifunction hemivariational inequalities

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In this paper, we consider and study a new class of hemivariational inequalities, which is called trifunction hemivariational inequality. We suggest and analyze a class of iterative methods for solving trifunction hemivariational inequalities using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pseudomonotonicity, which is a weaker condition than monotonicity. Results obtained in this paper include several new and known results as special cases.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Alvarez F., Attouch H.: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator damping. Set Valued Anal. 9, 3–11 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Clarke F.H., Ledyaev Y.S., Stern R.J., Wolenski P.R.: Nonsmooth Analysis and Control Theory. Springer, New York (1998)

    MATH  Google Scholar 

  3. Costea, N., Radulescu, V.: Hartman-Stampacchia results for stably pseudomonotone operators and non-linear hemivariational inequalities. Appl. Anal. 1–14, iFirst (2009)

  4. Carl S., Le V.K., Motreanu D.: Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications. Springer, Berlin (2007)

    MATH  Google Scholar 

  5. Crespi G.P., Ginchev J., Rocca M.: Existence of solutions and star-shapedness in Minty variational inequalities. J. Global Optim. 32, 485–494 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dem’yanov V.F., Stavroulakis G.E., Ployakova L.N., Panagiotopoulos P.D.: Quasidiffferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics. Kluwer, Dordrecht (1996)

    Google Scholar 

  7. Giannessi F., Maugeri A.: Variational Inequalities and Network Equilibrium Problems. Plenum Press, New York (1995)

    MATH  Google Scholar 

  8. Giannessi F., Maugeri A., Pardalos P.M.: Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. Kluwer, Dordrecht (2001)

    Google Scholar 

  9. Gilbert, R.P., Panagiotopoulos, P.D., Pardalos, P.M.: From Convexity to Nonconvexity. Kluwer, Holland

  10. Glowinski R., Lions J., Tremolieres R.: Numerical Analysis of Variational Inequalities. North- Holland, Amsterdam (1981)

    MATH  Google Scholar 

  11. Martinet B.: Regularization d’inequations variationnelles par approximation successive. Rev. Autom. Inform. Res. Oper. Serie Rouge 3, 154–159 (1970)

    MathSciNet  Google Scholar 

  12. Migorski S., Ochal A.: Hemivariational inequalities for stationary Navier–Stokes equations. J. Math. Anal. Appl. 306, 197–217 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Migorski S., Ochal A.: Boundary hemivariational inequality of parabolic type. Nonl. Anal. 57, 579–596 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Motreanu D., Radulescu V.: Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems. Kluwer, Dordrechet (2003)

    MATH  Google Scholar 

  15. Naniewicz Z., Panagiotopoulos P.D.: Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker, New York (1995)

    Google Scholar 

  16. Noor M.A.: New approximation schemes for general variational inequalities. J. Math. Anal. Appl 251, 217–229 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  17. Noor M.A.: Auxiliary principle technique for equilibrium problems. J. Optim. Theory Appl. 122, 371–386 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Noor M.A.: Some developments in general variational inequalities. Appl. Math. Comput. 152, 199–277 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Noor M.A.: Fundamentals of mixed quasi variational inequalities. Inter. J. Pure Appl. Math. 15, 137–258 (2004)

    MATH  Google Scholar 

  20. Noor M.A.: Hemivariational inequalities. J. Appl. Math. Comput. 17, 59–72 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Noor M.A.: Fundamentals of equilibrium problems. Math. Inequal. Appl. 9, 529–566 (2006)

    MATH  MathSciNet  Google Scholar 

  22. Noor, M.A., Noor, K.I., Huang, Z.Y.: Bifunction hemivariational inequalities. J. Appl. Math. Comput. (2010)

  23. Noor M.A., Noor K.I., Rassias Th.M.: Some aspects of variational inequalities. J. Comput. Appl. Math. 47, 285–312 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  24. Noor M.A., Oettli W.: On general nonlinear complementarity problems and quasi-equilibria. Le Mate. (Catania) 49, 313–331 (1994)

    MATH  MathSciNet  Google Scholar 

  25. Panagiotopoulos P.D.: Nonconvex energy functions, hemivariational inequalities and substationary principles. Acta. Mech. 42, 160–183 (1983)

    MathSciNet  Google Scholar 

  26. Panagiotopoulos P.D.: Hemivariational Inequalities, Applications to Mechanics and Engineering. Springer, Berlin (1993)

    Google Scholar 

  27. Pardalos P.M., Rassias T.M., Khan A.A.: Nonlinear Analysis and Variational Problems. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

  28. Stampacchia G.: Formes bilineaires coercivities sur les ensembles coercivities sur les ensembles convexes. C. R. Acad. Sci. Paris 258, 4413–4416 (1964)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

    Muhammad Aslam Noor & Khalida Inayat Noor

  2. Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia

    Muhammad Aslam Noor

Authors
  1. Muhammad Aslam Noor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Khalida Inayat Noor
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Aslam Noor.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Noor, M.A., Noor, K.I. Iterative schemes for trifunction hemivariational inequalities. Optim Lett 5, 273–282 (2011). https://doi.org/10.1007/s11590-010-0206-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-010-0206-x

Keywords

Search

Navigation