New unifying convergence criteria for Newton-like methods

Volume 29 / 2002

Ioannis K. Argyros Applicationes Mathematicae 29 (2002), 359-369 MSC: 65B05, 47H17, 49M15, 65G99, 65J15, 65N30, 65N35. DOI: 10.4064/am29-3-7


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.


  • Ioannis K. ArgyrosDepartment of Mathematics
    Cameron University
    Lawton, OK 73505, U.S.A.

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