On the approximation of the solutions of equations in Banach spaces by sequences

Let \(X\) be a Banach space, \(Y\) a normed space \(P:X\rightarrow Y\) a nonlinear operator and the equation \(P\left( x\right) =0\) with solution \(x^{\ast}\). Consider \(\Sigma:=\left( x_{n}\right) _{n\geq0}\) a sequence from \(X\) and define the convergence order of \(\Sigma\) with respect to the solution of equation \(P\left( x\right) =0\). We give a general result with sufficient conditions such that the sequence \(\Sigma\) converge to the solution \(x^{\ast}\) with a given convergence order.

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Original title (in French)

Sur l’approximation des solutions des equations à l’aide des suites à éléments dans un espace de Banach

English translation of the title

On the approximation of the solutions of equations in Banach spaces by sequences

approximation sequences; nonlinear equations in Banach spaces; convergence order.

Scanned paper (on the journal website).

PDF-Latex version of the paper.

I. Păvăloiu, Sur l’approximation des solutions des equations à l’aide des suites à éléments dans un espace de Banach, Anal. Numér. Théor. Approx., 5 (1976) no. 1, pp. 63-67 (in French).

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[3] Traub, J. F., Iterative Methods for the Solution of Equations. Prentice-Hall Inc. Englewood Cliffs N. J. (1964).