On the convergence of iterates to fixed points of analytic operators

Ioannis K. Argyros

doi:10.33993/jnaat331-754

Authors

Ioannis K. Argyros Cameron of University, Lawton, USA

DOI:

https://doi.org/10.33993/jnaat331-754

Keywords:

analytic operator, method of successive substitutions, Newton's method, fixed point, Fréchet derivative, radius of convergence, simple zero

Abstract views: 201

Abstract

The results in this study deal with the question: given that an analytic operator has fixed point, when is it true that iterates (under the operator) of nearby points converge to the fixed point? We take advantage of the analyticity of the operator to show that it is possible to enlarge the convergence radius for the method of successive substitutions or Newton's method. A numerical example is finally given to show that under our conditions there exists a wider choice of initial guesses than before.

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References

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