Skip to main content
SpringerLink
Log in

Iterative Algorithms for Mixed Equilibrium Problems, Strict Pseudocontractions and Monotone Mappings

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

Abstract

In this paper, we introduce some iterative algorithms for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a strict pseudocontraction and the set of solutions of a variational inequality for a monotone, Lipschitz continuous mapping. We obtain both weak and strong convergence theorems for the sequences generated by these processes in 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. Ceng, L.C., Yao, J.C.: A hybrid iterative scheme for mixed equilibrium problems and fixed point problems. J. Comput. Appl. Math. 214, 186–201 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bigi, G., Castellani, M., Kassay, G.: A dual view of equilibrium problems. J. Math. Anal. Appl. 342, 17–26 (2008)

    MATH  MathSciNet  Google Scholar 

  3. Flam, S.D., Antipin, A.S.: Equilibrium programming using proximal-like algorithms. Math. Program. 78, 29–41 (1997)

    Article  MathSciNet  Google Scholar 

  4. Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123–145 (1994)

    MATH  MathSciNet  Google Scholar 

  5. Browder, F.E., Petryshyn, W.V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. Math. Anal. Appl. 20, 197–228 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  6. Combettes, P.L., Hirstoaga, S.A.: Equilibrium programming in Hilbert spaces. J. Nonlinear Convex Anal. 6, 117–136 (2005)

    MATH  MathSciNet  Google Scholar 

  7. Takahashi, S., Takahashi, W.: Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces. J. Math. Anal. Appl. 331, 506–515 (2006)

    Article  Google Scholar 

  8. Su, Y., Shang, M., Qin, X.: An iterative method of solutions for equilibrium and optimization problems. Nonlinear Anal. (2007). doi:10.1016/j.na.2007.08.045

    Google Scholar 

  9. Tada, A., Takahashi, W.: Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. J. Optim. Theory Appl. 133, 359–370 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Plubtieng, S., Punpaeng, R.: A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings. Appl. Math. Comput. 197, 548–558 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Ceng, L.C., AI-Homidan, S., Ansari, Q.H., Yao, J.C.: An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings. J. Comput. Appl. Math. (2008). doi: 10.1016/j.cam.2008.03.032

    Google Scholar 

  12. Marino, G., Xu, H.K.: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 329, 336–346 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Zhou, H.Y.: Convergence theorems of fixed points for κ-strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 343, 546–556 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Peng, J.W., Yao, J.C.: A new hybrid-extragradient method for generalized mixed equilibrium problems and fixed point problems and variational inequality problems. Taiwan. J. Math. 12, 1401–1433 (2008)

    MATH  MathSciNet  Google Scholar 

  15. Takahashi, W., Toyoda, M.: Weak convergence theorems for nonexpansive mappings and monotone mappings. J. Optim. Theory Appl. 118, 417–428 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, China

    J. W. Peng

Authors
  1. J. W. Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. W. Peng.

Additional information

Communicated by F. Giannessi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peng, J.W. Iterative Algorithms for Mixed Equilibrium Problems, Strict Pseudocontractions and Monotone Mappings. J Optim Theory Appl 144, 107–119 (2010). https://doi.org/10.1007/s10957-009-9585-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-009-9585-5

Keywords

Search

Navigation