A sequential implicit function theorem for the chords iteration

✍ Scribed by Nedelcheva, Diana Kirilova

• Book ID: 121610410
• Publisher: SP Versita
• Year: 2013
• Tongue: English
• Weight: 244 KB
• Volume: 63
• Category: Article
• ISSN: 0139-9918
• DOI: 10.2478/s12175-013-0157-7

✦ Synopsis

In this paper we study the local convergence of the method

in order to find the solution of the generalized equation

We first show that under the strong metric regularity of the linearization of the associated mapping and some additional assumptions regarding dependence on the parameter and the relation between the operator A and the Jacobian ∇ x f (p, x), we prove linear convergence of the method which is uniform in the parameter p. Then we go a step further and obtain a sequential implicit function theorem describing the dependence of the set of sequences of iterates of the parameter.