International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2557

Study on unified implicit methods for solving variational inequalities

Muhammad Aslam Noor1*, Khalida Inayat Noor1, Saira Zainab1 and Eisa Al-said2      
1Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan. 2Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia.  
Email: [email protected]

  •  Accepted: 05 December 2011
  •  Published: 09 January 2012

Abstract

In this paper, we suggest and analyze some new implicit methods for solving the variational inequalities. These new methods include the extra gradient method of Korpelevich (1976) and the modified extra gradient method of Noor (2004, 2010) as special cases. We also consider the convergence of this new implicit iterative method under some conditions. The ideas and techniques of this paper may stimulate further research in this dynamic area of pure and applied sciences.

 

Key words: Variational inequality, implicit iterative method, convergence.