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All issues Volume 47 / No 1 (January-February 2013) ESAIM: M2AN, 47 1 (2013) 149-167 References
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Issue
ESAIM: M2AN
Volume 47, Number 1, January-February 2013
Page(s) 149 - 167
DOI https://doi.org/10.1051/m2an/2012026
Published online 31 July 2012
  1. S. Amat and S. Busquier, Third-order iterative methods under Kantorovich conditions. J. Math. Anal. Appl. 336 (2007) 243–261. [CrossRef] [Google Scholar]
  2. S. Amat, C. Bermúdez, S. Busquier and D. Mestiri, A family of Halley-Chebyshev iterative schemes for non-Fréechet differentiable operators. J. Comput. Appl. Math. 228 (2009) 486–493. [CrossRef] [Google Scholar]
  3. I.K. Argyros, A Newton–Kantorovich theorem for equations involving m-Fréchet differentiable operators and applications in radiative transfer. J. Comput. Appl. Math. 131 (2001) 149–159. [CrossRef] [Google Scholar]
  4. I.K. Argyros, An improved convergence analysis and applications for Newton-like methods in Banach space, Numer. Funct. Anal. Optim. 24 (2003) 653–572. [CrossRef] [MathSciNet] [Google Scholar]
  5. I.K. Argyros, On the Newton-Kantorovich hypothesis for solving equations. J. Comput. Appl. Math. 169 (2004) 315–332. [CrossRef] [Google Scholar]
  6. D.D. Bruns and J.E. Bailey, Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state. Chem. Eng. Sci. 32 (1977) 257–264. [CrossRef] [Google Scholar]
  7. K. Deimling, Nonlinear functional analysis. Springer-Verlag, Berlin (1985). [Google Scholar]
  8. J.A. Ezquerro and M.A. Hernández, Generalized differentiability conditions for Newton’s method. IMA J. Numer. Anal. 22 (2002) 187–205. [CrossRef] [MathSciNet] [Google Scholar]
  9. J.A. Ezquerro and M.A. Hernández, On an application of Newton’s method to nonlinear operators with ω-conditioned second derivative. BIT 42 (2002) 519–530. [MathSciNet] [Google Scholar]
  10. J.A. Ezquerro and M.A. Hernández, Halley’s method for operators with unbounded second derivative. Appl. Numer. Math. 57 (2007) 354–360. [CrossRef] [Google Scholar]
  11. J.A. Ezquerro, D. González and M.A. Hernández, Majorizing sequences for Newton’s method from initial value problems. J. Comput. Appl. Math. (submitted). [Google Scholar]
  12. M. Ganesh and M.C. Joshi, Numerical solvability of Hammerstein integral equations of mixed type. IMA J. Numer. Anal. 11 (1991) 21–31. [CrossRef] [MathSciNet] [Google Scholar]
  13. J.M. Gutiérrez, A new semilocal convergence theorem for Newton’s method. J. Comput. Appl. Math. 79 (1997) 131–145. [CrossRef] [Google Scholar]
  14. L.V. Kantorovich, On Newton’s method for functional equations. Dokl Akad. Nauk SSSR 59 (1948) 1237–1240 (in Russian). [Google Scholar]
  15. L.V. Kantorovich, The majorant principle and Newton’s method. Dokl. Akad. Nauk SSSR 76 (1951) 17–20 (in Russian). [Google Scholar]
  16. L.V. Kantorovich and G.P. Akilov, Functional analysis. Pergamon Press, Oxford (1982). [Google Scholar]
  17. A.M. Ostrowski, Solution of equations in Euclidean and Banach spaces. London, Academic Press (1943). [Google Scholar]
  18. F.A. Potra and V. Pták, Sharp error bounds for Newton process. Numer. Math. 34 (1980) 63–72. [CrossRef] [MathSciNet] [Google Scholar]
  19. J. Rashidinia and M. Zarebnia, New approach for numerical solution of Hammerstein integral equations. Appl. Math. Comput. 185 (2007) 147–154. [CrossRef] [Google Scholar]
  20. W.C. Rheinboldt, A unified convergence theory for a class of iterative processes. SIAM J. Numer. Anal. 5 (1968) 42–63. [CrossRef] [MathSciNet] [Google Scholar]
  21. T. Yamamoto, Convergence theorem for Newton-like methods in Banach spaces. Numer. Math. 51 (1987) 545–557. [CrossRef] [MathSciNet] [Google Scholar]
  22. Z. Zhang, A note on weaker convergence conditions for Newton iteration. J. Zhejiang Univ. Sci. Ed. 30 (2003) 133–135, 144 (in Chinese). [MathSciNet] [Google Scholar]

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