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Iterative solution of nonlinear equations involving set-valued uniformly accretive operators. (English) Zbl 1060.47511
Summary: Let E be a real normed linear space and let A:E2 E be a uniformly continuous and uniformly quasi-accretive multivalued map with nonempty closed values such that the range of (I-A) is bounded and the inclusion fAx has a solution x * E. It is proved that the Ishikawa and Mann type iteration processes converge strongly to x * . Further, if T:E2 E is a uniformly continuous and uniformly hemicontractive set-valued map with bounded range and a fixed point x * E, it is proved that both the Mann and Ishikawa type iteration processes converge strongly to x * . The strong convergence of these iteration processes with errors is also proved.
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H06Accretive operators, dissipative operators, etc. (nonlinear)
65J15Equations with nonlinear operators (numerical methods)
47H04Set-valued operators