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Iterative processes with errors for nonlinear equations. (English) Zbl 1071.47061

Let \(D\) be a nonempty subset of a Banach space \(X\) and \(T:D \to 2^X\) be a multivalued operator of generalized monotone type such that \(T(D)\) is bounded and \(F(T):= \{x \in D | x \in T(x)\}\) is nonempty. Some new convergence theorems for the Ishikawa and Mann iteration processes with errors to a fixed point of \(T\) are given.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H04 Set-valued operators
47H10 Fixed-point theorems
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