Geodesic
New unifying convergence criteria for Newton-like methods
Ioannis K. Argyros1
1 Department of Mathematics Cameron University Lawton, OK 73505, U.S.A.
Applicationes Mathematicae, Tome 29 (2002) no. 3, pp. 359-369 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the “majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence radius.
DOI : 10.4064/am29-3-7
Keywords: present local semilocal analysis newton like methods banach space hypotheses operators involved general turns out choosing special cases majorizing functions obtain previous results literature vice versa since results deeper insight structure functions involved obtain semilocal convergence under weaker conditions local convergence larger convergence radius

Ioannis K. Argyros 1

1 Department of Mathematics Cameron University Lawton, OK 73505, U.S.A. 
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Ioannis K. Argyros. New unifying convergence criteria
  for Newton-like methods. Applicationes Mathematicae, Tome 29 (2002) no. 3, pp. 359-369. doi: 10.4064/am29-3-7

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