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Relaxed extragradient methods with regularization for general system of variational inequalities with constraints of split feasibility and fixed point problems. (English) Zbl 1272.49061

Summary: We suggest and analyze relaxed extragradient iterative algorithms with regularization for finding a common element of the solution set of a general system of variational inequalities, the solution set of a split feasibility problem, and the fixed-point set of a strictly pseudocontractive mapping defined on a real Hilbert space. Here, the relaxed extragradient methods with regularization are based on the well-known successive approximation method, extragradient method, viscosity approximation method, regularization method, and so on. Strong convergence of the proposed algorithms under some mild conditions is established. Our results represent the supplementation, improvement, extension, and development of the corresponding results in the very recent literature.

MSC:

49M30 Other numerical methods in calculus of variations (MSC2010)
49J40 Variational inequalities
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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