Fixed point iteration for pseudocontractive maps. (English) Zbl 0913.47052
Summary: Let be a compact convex subset of a real Hilbert space , a continuous pseudocontractive map. Let , , , , and be real sequences in [0,1] satisfying appropriate conditions. For arbitrary , define the sequence iteratively by ; , where , are arbitrary sequences in . Then, converges strongly to a fixed point of . A related result deals with the convergence of to a fixed point of when is Lipschitz and pseudocontractive. Our theorems also hold for the slightly more general class of continuous hemicontractive nonlinear maps.
|47H10||Fixed point theorems for nonlinear operators on topological linear spaces|
|47H05||Monotone operators (with respect to duality) and generalizations|
|47J05||Equations involving nonlinear operators (general)|
|47H06||Accretive operators, dissipative operators, etc. (nonlinear)|