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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 $\phi$-strongly accretive multivalued map with nonempty closed convex values such that the inclusion $0\in Ax$ 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 $\phi$-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
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References:
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