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In this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping… (More)
In this paper, we use the auxiliary principle technique coupled with the principle of iterative regularization to suggest and analyze some new iterative algorithms for solving mixed quasi variational inequalities. We also study the convergence criteria of these algorithms under some suitable and mild conditions. Several special cases are also considered.… (More)
Copyright q 2012 Muhammad Aslam Noor et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We use auxiliary principle technique coupled with iterative regularization method to suggest and… (More)
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… (More)
In this paper, we show that the general variational inequalities are equivalent to a new class of general Wiener-Hopf equations involving the nonexpansive mappings. Using this equivalence, we suggest and analyze an iterative method for finding the common elements of the solution set of the general variational inequalities and the solution set of the… (More)
We use the auxiliary principle technique to suggest and analyze an implicit method for solving the equilibrium problems on Hadamard manifolds. The convergence of this new implicit method requires only the speudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered.