Geodesic
Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods
Applications of Mathematics, Tome 28 (1983) no. 1, pp. 21-31.

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First, a result of J. W. Schmidt about the monotone enclosure of solutions of nonlinear equations is generalized. Then an iteration method is considered, which is more effective than other known methods. For this method, monotone enclosure statements are also proved.
DOI : 10.21136/AM.1983.103999
Classification : 47H07, 47J25, 65J15
Keywords: derivative free methods; upper and lower bounds; partially ordered Banach spaces; monotone enclosure of solutions; Regula-falsi-like methods; generalized divided difference operators; existence; convergence; numerical example; iterative method 
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Schneider, Norbert. Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods. Applications of Mathematics, Tome 28 (1983) no. 1, pp. 21-31. doi : 10.21136/AM.1983.103999. http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.103999/

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