East Asian mathematical journal
- 제24권3호
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- Pages.289-293
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- 2008
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- 1226-6973(pISSN)
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- 2287-2833(eISSN)
ON THE NEWTON-KANTOROVICH AND MIRANDA THEOREMS
초록
We recently showed in [5] a semilocal convergence theorem that guarantees convergence of Newton's method to a locally unique solution of a nonlinear equation under hypotheses weaker than those of the Newton-Kantorovich theorem [7]. Here, we first weaken Miranda's theorem [1], [9], [10], which is a generalization of the intermediate value theorem. Then, we show that operators satisfying the weakened Newton-Kantorovich conditions satisfy those of the weakened Miranda’s theorem.
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