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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 \(T: K\to K\) 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:

47H10 Fixed-point theorems
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H05 Monotone operators and generalizations
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