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A Newton-like method for generalized operator equations in Banach spaces.
- Source :
-
Numerical Algorithms . Oct2014, Vol. 67 Issue 2, p289-303. 15p. - Publication Year :
- 2014
-
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, ) 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, ). 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 67
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 98581499
- Full Text :
- https://doi.org/10.1007/s11075-013-9791-y