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Generalized differentiability conditions for Newton’s method. (English) Zbl 1006.65051
The authors provide an alternative technique to majorizing sequences, in which particular real sequences are also constructed, but they are not majorizing ones. The domains of existence and uniqueness of the solution are also obtained. Moreover, the authors generalize the result obtained under Newton-Kantorovich type conditions. An application of the obtained semilocal convergence results to a nonlinear Hammerstein integral equations of the second kind is given.

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
45G10 Other nonlinear integral equations
65R20 Numerical methods for integral equations
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