A weaker affine covariant Newton–Mysovskikh theorem for solving equations

Volume 33 / 2006

Ioannis K. Argyros Applicationes Mathematicae 33 (2006), 355-363 MSC: 65H10, 65G99, 65J15, 47H17, 49M15. DOI: 10.4064/am33-3-9


The Newton–Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical examples are also provided.


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

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