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Solving variational inequalities involving nonexpansive type mappings. (English) Zbl 1182.47050

In this paper, the existence of solutions for a certain class of variational inequalities \(VI_D(C,I-f)\) involving nonexpansive type mappings in smooth Banach spaces are investigated. The main results are: the existence of a common element of \(D\) and \(VI_D(C,I-f)\) when \(f\) is weakly contractive; the existence of solutions of variational inequalities \(VI_D(C,I-f)\) with \(f\) is nonexpansive or pseudocontractive; an iterative algorithm for finding solutions of variational inequalities of \(VI_D(C,I-f)\) when \(f\) is weakly contractive or nonexpansive. The problems of finding a common fixed point of nonexpansive mappings and finding a common zero of accretive operators also are considered.

MSC:

47J20 Variational and other types of inequalities involving nonlinear operators (general)
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H10 Fixed-point theorems
47J25 Iterative procedures involving nonlinear operators
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