Projection Iterative Schemes for General Variational Inequalities

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities

We suggest and analyze some implicit iterative methods for solving the extended general nonconvex variational inequalities using the projection technique. We show that the convergence of these iterative methods requires only the gh-pseudomonotonicity, which is a weaker condition than gh-monotonicity. We also discuss several special cases. Our method of proof is very simple as compared with othe...

Projection Iterative Methods for Multivalued General Variational Inequalities

In this paper, we introduce a new class of variational inequalities involving two operators. Using the projection technique, we establish the equivalence between the multivalued general variational inequalities and the fixed point problems. This equivalent formulation is used to suggest and analyze some iterative algorithms for solving the multivalued general variational inequalities. We also d...

Projection Iterative Approximations for a New Class of General Random Implicit Quasi-variational Inequalities

We introduce a class of projection-contraction methods for solving a class of general random implicit quasi-variational inequalities with random multivalued mappings in Hilbert spaces, construct some random iterative algorithms, and give some existence theorems of random solutions for this class of general random implicit quasi-variational inequalities. We also discuss the convergence and stabi...

System of General Variational Inequalities Involving Different Nonlinear Operators Related to Fixed Point Problems and Its Applications

By using the projection methods, we suggest and analyze the iterative schemes for finding the approximation solvability of a system of general variational inequalities involving different nonlinear operators in the framework of Hilbert spaces. Moreover, such solutions are also fixed points of a Lipschitz mapping. Some interesting cases and examples of applying the main results are discussed and...