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Convergence analysis of parallel \(S\)-iteration process for system of generalized variational inequalities. (English) Zbl 1377.49010
Summary: We consider a new System of Generalized Variational Inequalities (SGVI) defined on two closed convex subsets of a real Hilbert space. To find the solution of considered SGVI, a parallel Mann iteration process and a parallel \(S\)-iteration process have been proposed and the strong convergence of the sequences generated by these parallel iteration processes is discussed. Numerical example illustrates that the proposed parallel \(S\)-iteration process has an advantage over parallel Mann iteration process in computing altering points of some mappings.

MSC:
49J40 Variational inequalities
47J25 Iterative procedures involving nonlinear operators
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