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On a system of generalized nonlinear variational inequalities. (English) Zbl 1076.49005
Summary: We introduce and study a new class of systems of generalized nonlinear variational inequalities involving strongly monotone mappings in Hilbert spaces. Using the projection method, we establish an equivalence between the system of generalized nonlinear variational inequalities and the fixed-point problem. This equivalence is used to investigate the existence and uniqueness of solutions of the system of generalized nonlinear variational inequalities and suggest new iterative algorithms for computing the approximate solutions. The convergence and stability analysis are also studied.
MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
47H10Fixed point theorems for nonlinear operators on topological linear spaces