Abstract
In this paper, we are concerned with the semilocal convergence analysis of a Newton-like method discussed by Bartle (Amer Math Soc 6: 827---831, 1955) to solve the generalized operator equations containing nondifferentiatble term in Banach spaces. This method has also been studied by Rheinboldt (SIAM J Numer Anal 5: 42---63, 1968). The aim of the paper is to discuss the convergence analysis under local Lipschitz condition ? F x ? ? F x 0 ? ? ≤ ? ( ? x ? x 0 ? ) $\|F'_{x}-F'_{x_{0}}\|\le \omega (\|x-x_{0}\|)$ for a given point x 0 $x_{0}$ . Our results extend and improve the previous ones in the sense of local Lipschitz conditions. We apply our results to solve the Fredholm-type operator equations.
Published Version
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