Steepest descent method for equilibrium points of nonlinear systems with accretive operators.

*(English)*Zbl 0979.47036Let $E$ be a normed linear space and let $A$ be a bounded uniformly continuous $\varphi $-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 $\varphi $-strongly pseudocontractive maps. Some possible generalizations of the approximation method are also considered.

Reviewer: Marco Biroli (Monza)

##### MSC:

47H06 | Accretive operators, dissipative operators, etc. (nonlinear) |

47J25 | Iterative procedures (nonlinear operator equations) |

47J05 | Equations involving nonlinear operators (general) |

65Q05 | Numerical methods for functional equations (MSC2000) |

47H04 | Set-valued operators |