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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.

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