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Zbl 0979.47036
Chidume, C.E.; Moore, Chika
Steepest descent method for equilibrium points of nonlinear systems with accretive operators.
(English)
[J] J. Math. Anal. Appl. 245, No.1, 142-160 (2000). ISSN 0022-247X

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 $x^*$.\par 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.
[Marco Biroli (Monza)]
MSC 2000:
*47H06 Accretive operators, etc. (nonlinear)
47J25 Methods for solving nonlinear operator equations (general)
47J05 Equations involving nonlinear operators (general)
65Q05 Numerical methods for functional equations
47H04 Set-valued operators

Keywords: steepest descent method; equilibrium points; $\phi$-strongly accretive multivalued map; Ishikawa and Mann iteration; $\phi$-strongly pseudocontractive maps; approximation method

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