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1	Inverse strongly monotone operators and variational inequalities Chi, Wen-te 23 June 2009 (has links) In this paper, we report existing convergence results on monotone variational inequalities where the governing monotone operators are either strongly monotone or inverse strongly monotone. We reformulate the variational inequality problem as an equivalent fixed point problem and then use fixed point iteration method to solve the original variational inequality problem. In the case of strong monotonicity case we use the Banach¡¦s contraction principle to define out iteration sequence; while in the case of inverse strong monotonicity we use the technique of averaged mappings to define our iteration sequence. In both cases we prove strong convergence for our iteration methods. An application to a minimization problem is also included. convergence iteration projection minimization Lipschitzian operator Variational inequality inverse strongly monotone averaged mapping strongly monotone monotone fixed point