References
- Appell , J. , De Pascale , E. , Lysenko , Ju. V. and Zabreiko , P. P. 1997 . New results on Newton–Kantorovich approximations with applications to nonlinear integral equations . Numer. Funct. Anal. Optim. , 18 ( 1&2 ) : 1 – 18 .
- Cianciaruso , F. and De Pascale , E. 2002 . The Newton–Kantorovich approximations for the nonlinear integro-differential equations of mixed type . Ric. Mat. LI fasc. , 2 (to appear)
- Demidovich , N. T. , Zabreiko , P. P. and Lysenko , Ju. V. 1993 . Some remarks on the Newton–Kantorovich method for nonlinear equations with Hölder continuous linearizations . Izv. Akad. Nauk. Beloruss , 3 : 22 – 26 . (in Russian)
- De Pascale , E. and Zabreiko , P. P. 1998 . The convergence of the Newton–Kantorovich method under Vertgeim conditions: a new improvement . Z. Anal. Anwend. , 17 ( No. 2 ) : 271 – 280 .
- Fenyö , I. 1954 . Über die lösung der in Banachschen raume definierten nichtlinearen gleichungen . Acta. Math. Acad. Sci. Hungar. , 5 : 85 – 93 .
- Kantorovich , L. V. and Akilov , G. P. 1982 . “ Functional analysis (in Russian) ” . Nauka, Moscow [(1982). Engl. Transl.: Pergamon Press, Oxford]
- Krasnosel'skij , M. A. , Vajnikko , G. M. , Zabreiko , P. P. , Rutitskij , Ja. B. and Stetsenko , V. Ja. 1966 . “ Approximate solutions of operator equations (in Russian) ” . Nauka, Moscow [(1972). Engl. Transl.: Noordhoff–Groningen]
- Lysenko , J. V. 1994 . Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations . Dokl. Akad. Nauk BSSR , 38 : 20 – 24 . (in Russian)
- Vertgeim , B. A. 1956 . On conditions for the applicability of Newton's method . Dokl. Akad. Nauk. SSSR , 110 : 719 – 722 . (in Russian)
- Vertgeim , B. A. 1957 . On some methods of the approximate solution of nonlinear functional equations in Banach spaces . Uspekhi Mat. Nauk. , 12 : 166 – 169 . (in Russian), [(1960). Engl. Transl.: Amer. Math. Soc. Transl. 16(2):378-382]
- Yamamoto , T. 2000 . Historical developments in convergence analysis for Newton's and Newton-like methods . J. Comput. Appl. Math. , 124 : 1 – 23 .
- Zabreiko , P. P. and Nguen , D. F. 1987 . The majorant method in the theory of Newton–Kantorovich approximations and the Pták error estimates . Numer. Funct. Anal. and Optimiz. , 9 ( 5&6 ) : 671 – 684 .