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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
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.
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