Skip to main content
Log in

A note on Ceng-Wang-Yao’s result [Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Meth. Oper. Res. (2008) 67: 375–390]

  • Original Article
  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

In this paper, we give a short and simple proof of the recent result of Ceng et al. (Math Methods Oper Res 67(3):375–390, 2008).

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ceng LC, Wang CY, Yao JC (2008) Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities. Math Methods Oper Res 67(3): 375–390

    Article  MathSciNet  MATH  Google Scholar 

  • Chancelier JP (2009) Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces. J Math Anal Appl 353(1): 141–153

    Article  MathSciNet  MATH  Google Scholar 

  • Chidume CE, Chidume CO (2006) Iterative approximation of fixed points of nonexpansive mappings. J Math Anal Appl 318(1): 288–295

    Article  MathSciNet  MATH  Google Scholar 

  • Korpelevič GM (1976) An extragradient method for finding saddle points and for other problems. (Russian) Èkonom. i Mat. Metody 12(4): 747–756

    MathSciNet  MATH  Google Scholar 

  • Nadezhkina N, Takahashi W (2006) Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings. J Optim Theor Appl 128(1): 191–201

    Article  MathSciNet  MATH  Google Scholar 

  • Suzuki T (2007) A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings. Proc Am Math Soc 135(1): 99–106

    Article  MATH  Google Scholar 

  • Takahashi W (2000) Nonlinear functional analysis. Fixed point theory and its applications, Yokohama Publishers, Yokohama, p iv+276

    MATH  Google Scholar 

  • Takahashi W, Toyoda M (2003) Weak convergence theorems for nonexpansive mappings and monotone mappings. J Optim Theor Appl 118(2): 417–428

    Article  MathSciNet  MATH  Google Scholar 

  • Verma RU (1999) On a new system of nonlinear variational inequalities and associated iterative algorithms. Math Sci Res Hot-Line 3(8): 65–68

    MathSciNet  MATH  Google Scholar 

  • Yao Y, Yao JC (2007) On modified iterative method for nonexpansive mappings and monotone mappings. Appl Math Comput 186(2): 1551–1558

    Article  MathSciNet  MATH  Google Scholar 

  • Zeng LC, Yao JC (2006) Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems. Taiwan J Math 10(5): 1293–1303

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Satit Saejung.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saejung, S., Wongchan, K. A note on Ceng-Wang-Yao’s result [Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Meth. Oper. Res. (2008) 67: 375–390]. Math Meth Oper Res 73, 153–157 (2011). https://doi.org/10.1007/s00186-010-0339-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00186-010-0339-9

Keywords

Navigation