Geodesic
On Brown's method with convexity hypotheses
Applications of Mathematics, Tome 49 (2004) no. 2, pp. 165-184.

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Given two initial points generating monotone convergent Brown iterations in the context of the monotone Newton theorem (MNT), it is proved that if one of them is an upper bound of the other, then the same holds for each pair of respective terms in the Brown sequences they generate. This comparison result is carried over to the corresponding Brown-Fourier iterations. An illustration is discussed.
DOI : 10.1023/B:APOM.0000027222.62203.3c
Classification : 65H10
Keywords: nonlinear systems; convex functions; Brown’s method; monotone convergence; Fourier iterates 
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Milaszewicz, Juan Pedro. On Brown's method with convexity hypotheses. Applications of Mathematics, Tome 49 (2004) no. 2, pp. 165-184. doi : 10.1023/B:APOM.0000027222.62203.3c. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000027222.62203.3c/

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