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Averaging techniques and cocoercively monotone mappings. (English) Zbl 1152.49011

Summary: Based on the convergence of averaging techniques for relaxation algorithms and for their specialization as projection methods and auxiliary problem principle, the solvability of a class of variational inequalities involving cocoercively monotone mappings is explored. The notion of the cocoercively monotone mapping is weaker than other existing notions studied in literature, including the cocoercive and strongly monotone mappings.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49M20 Numerical methods of relaxation type
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