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On modified iterative method for nonexpansive mappings and monotone mappings. (English) Zbl 1121.65064
Let \(C\) be a nonempty, closed, convex subset of a real Hilbert space \(H\) and let \(A:C\to H\) be an inverse-strongly monotone mapping. Moreover, let \(S:C\to C\) be nonexpansive. The authors study a new class of iteration schemes for finding a fixed-point \(x^*\) of \(S\) that also fulfills the variational inequality \(\langle Ax^*, v-x^*\rangle \geq 0\) for all \(v\in C\). Results on the strong convergence of the sequence of iterates are proven. Also the case \(A=I-T\) with a pseudocontractive mapping \(T:C\to C\) is considered.

MSC:
65J15 Numerical solutions to equations with nonlinear operators
47H05 Monotone operators and generalizations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
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