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We present a new sufficient semilocal convergence conditions for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. Thi s way, we expand the applicability of these methods in cases not covered in other studies such as Dennis (1971) [12], Ezquerro et al. (2000, 2010) [13,14], Kornstaedt (1975) [18], Potra and Pták (1984) [24], Potra (1985,...
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