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 \(\|F'_{x}-F'_{x_{0}}\|\le \omega (\|x-x_{0}\|)\) for a given point \(x_{0}\). 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.
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Sahu, D., Singh, K.K. & Singh, V.K. A Newton-like method for generalized operator equations in Banach spaces. Numer Algor 67, 289–303 (2014). https://doi.org/10.1007/s11075-013-9791-y
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DOI: https://doi.org/10.1007/s11075-013-9791-y
Keywords
- Banach space
- Generalized operator equation
- Fréchet derivative
- Newton-like method
- Semilocal convergence
- Nonlinear Fredholm-type operator equation