# A multipoint iterative method for semistable solutions

Abstract : This paper deals with variational inclusions of the form : $0\in \varphi(z)+F(z)$ where $\varphi$ is a single-valued function admitting a second order Fréchet derivative and $F$ is a set-valued map from $\R^q$ to the closed subsets of $\R^q$. In order to approximate a solution $\bar z$ of the previous inclusion, we use an iterative scheme based on a multipoint method. We obtain, thanks to some semistability properties of $\bar z$, local superquadratic or cubic convergent sequences
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https://hal.archives-ouvertes.fr/hal-00728816
Contributor : Célia Jean-Alexis <>
Submitted on : Thursday, September 6, 2012 - 4:49:04 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:27 PM

### Identifiers

• HAL Id : hal-00728816, version 1

### Citation

Burnet Steeve, Célia Jean-Alexis, Alain Piétrus. A multipoint iterative method for semistable solutions. Applied Mathematics E - Notes, Tsing Hua University, 2012, 12, pp.44-52. ⟨hal-00728816⟩

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