Abstract
In this paper, we introduce the concept of well-posedness for general variational inequalities and obtain some results under pseudomonotonicity. It is well known that monotonicity implies pseudomonotonicity, but the converse is not true. In this respect, our results represent an improvement and refinement of the previous known results. Since the general variational inequalities include (quasi) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems.
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Prof. Dr. Muhammad Aslam Noor received his M. Sc from Panjab University (Pakistan, 1967), M. Sc from Queen's University (Canada, 1971) and Ph. D from Brunel University (London, U. K. 1975). He became professor in 1985. He has taught several courses including variational inequalities, numerical analysis, finite element analysis, optimization and operations research in Iran, Pakistan, Saudi Arabia, Canada and UAE. He has published more than 290 research papers in international journals. He is a member of editorial boards of several scientific journals.
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Noor, M.A. Well-posed variational inequalities. JAMC 11, 165–172 (2003). https://doi.org/10.1007/BF02935729
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DOI: https://doi.org/10.1007/BF02935729