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Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations. (English) Zbl 0958.47030
Let K be a closed convex nonempty subset of a Hilbert space H and let T:KK be a Lipschitz pseudocontraction mapping with a nonempty set of fixed points. Weak and strong convergence theorems for iterative approximations of fixed points are proved. Some applications to monotone operators in Hilbert spaces are presented.
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H05Monotone operators (with respect to duality) and generalizations