On nonconvex bifunction variational inequalities |
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Authors: | Muhammad Aslam Noor Khalida Inayat Noor Eisa Al-Said |
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Affiliation: | 1. Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan 2. Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia
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Abstract: | In this paper, we introduce and consider a new class of variational inequalities, which is called the nonconvex bifunction variational inequality. We suggest and analyze some iterative methods for solving nonconvex bifunction variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only pseudomonotonicity, which is weaker condition than monotonicity. Our proof of convergence is very simple. Results proved in this paper may stimulate further research in this dynamic field. |
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