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Steepest descent method for equilibrium points of nonlinear systems with accretive operators. (English) Zbl 0979.47036

Let E be a normed linear space and let A be a bounded uniformly continuous φ-strongly accretive multivalued map with nonempty closed convex values such that the inclusion 0Ax has a solution x * .

The authors prove the strong convergence to x * of both Ishikawa and Mann iteration processes. The methods are also applies to the approximation of fixed points of φ-strongly pseudocontractive maps. Some possible generalizations of the approximation method are also considered.

MSC:
47H06Accretive operators, dissipative operators, etc. (nonlinear)
47J25Iterative procedures (nonlinear operator equations)
47J05Equations involving nonlinear operators (general)
65Q05Numerical methods for functional equations (MSC2000)
47H04Set-valued operators