Saira Zainab

Mixed quasi complementarity problems in topological vector spaces

In this paper, we introduce and consider a new class of complementarity problems, which is called the mixed quasi complementarity problems in a topological vector space. We show that the mixed quasi complementarity problems are equivalent to the mixed quasi variational inequalities. Using the KKM mapping theorem, we study the existence of a solution of the mixed quasi variational inequalities and mixed quasi complementarity problems. Several special cases are also discussed. Results obtained in this paper can be viewed as extension and generalization of the previously known results.

Implicit Methods for Equilibrium Problems on Hadamard Manifolds

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.

Some iterative algorithms for solving regularized mixed quasi variational inequalities

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. Results obtained in this paper continue to hold for these special cases.

Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities

We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex bifunction equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only monotonicity. Some special cases are also considered. Our proof of convergence is very simple. Results proved in this paper may stimulate further research in this dynamic field.

Regularized Mixed Variational-Like Inequalities

We use auxiliary principle technique coupled with iterative regularization method to suggest and analyze some new iterative methods for solving mixed variational-like inequalities. The convergence analysis of these new iterative schemes is considered under some suitable conditions. Some special cases are also discussed. Our method of proofs is very simple as compared with other methods. Our results represent a significant refinement of the previously known results.