Letter to the editor: On a unified implicit method for variational inequalities

Authors:
Muhammad Aslam Noor;Khalida Inayat Noor;Abdellah Bnouhachem
Affiliations:
Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan;Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan;Ibn Zohr University, ENSA, BP 1136, Agadir, Morocco
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

It is well known that variational inequalities are equivalent to fixed point problems. We use this equivalent formulation to suggest and analyze a new unified implicit method of solving variational inequalities. This new method includes several known implicit and extragradient methods as special cases. We prove that the convergence of this new method requires only the pseudomonotonicity of the operator, which is a weaker condition than monotonicity. Several special cases are discussed. An example is given to illustrate the implementation of the proposed method. A comparison with other methods shows that the present method performs better.