## Abstract

Let \(X\) be a Banach space, \(Y\) a normed space and the nonlinear operator equation \(P\left( x\right) =0\), where \(P:X\rightarrow Y\). We consider two operators \(Q_{1},Q_{2}:X\rightarrow X\) attached to \(P\) and we study the convergence of the Steffensen type method \[x_{n+1}=Q_1(x_n)-[Q_1( x_n), Q_2( x_n);P]^{-1}P(Q_1(x_n)). \] We give some conditions ensuring the convergence of this sequence to the solution and we obtain the convergence order of the sequence in terms of the convergence orders of \(Q_{1}\) and \(Q_{2}\).

## Authors

Ion Păvăloiu

## Title

### Original title (in French)

*Sur une méthode de type Steffensen utilisée pour la résolution des equations operationnelles non-linéaires*

### English translation of the title

*On a Steffensen type method for solving nonlinear operator equations*

## Keywords

Steffensen type method; Banach space; iterative method; convergence order

## References

[1] Pavaloiu, I., *Asupra operatorilor iterativi*, Studii si Cercetari Matematice, 23 (1971), 10, 1537–1544.

[2] Pavaloiu, I., *Introducere in teoria aproximarii solutiilor ecuatiilor*, Ed. Dacia, 1976.

[3] Ul’m, S., *Ob oboboscennyh rezdelennih reznostiak I*, Izv. Akad. Nauk Estonskoi SSR 16 (1867), 1, 13–36.

## About this paper

##### Cite this paper as:

I. Păvăloiu, *Sur une méthode de type Steffensen utilisée pour la résolution des equations operationnelles non-linéaires*, Seminar on functional analysis and numerical methods, Preprint no. 1 (1989), pp. 105-110 (in French).

##### Journal

Seminar on functional analysis and numerical methods,

Preprint

##### Publisher Name

“Babes-Bolyai” University,

Faculty of Mathematics,

Research Seminars

##### DOI

Not available yet.