The approximation of the solutions of equations using approximant sequences

Adrian Diaconu

doi:10.33993/jnaat321-731

Authors

Adrian Diaconu “Babes-Bolyai” University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat321-731

Keywords:

convergence of the approximant sequences for operatorial equations in Banach spaces

Abstract views: 207

Abstract

We intend to characterize the convergence of a certain sequence that belongs to a subset of a Banach space towards the solution of an equation obtained by the annulment of a nonlinear mapping that is defined on this subset and that takes values in another linear normed space. This mapping has a Fréchet derivative of a certain order which verifies the Lipschitz condition. We can establish some conditions that are enough both for the existence of the equation's solution and for a speed of convergence of a certain order for the approximant sequence.

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References

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