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The viscosity approximation process for quasi-nonexpansive mappings in Hilbert spaces. (English) Zbl 1189.49011

Summary: We discuss the strong convergence of the viscosity approximation method, in Hilbert spaces, relatively to the computation of fixed points of operators in the wide class of quasi-nonexpansive mappings. Our convergence results improve previously known ones obtained for the class of nonexpansive mappings.

MSC:

49J40 Variational inequalities
65J15 Numerical solutions to equations with nonlinear operators
65K15 Numerical methods for variational inequalities and related problems
47J25 Iterative procedures involving nonlinear operators
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