Geodesic
Ostrowski-Kantorovich theorem and $S$-order of convergence of Halley method in Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 153-163.

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Ostrowski-Kantorovich theorem of Halley method for solving nonlinear operator equations in Banach spaces is presented. The complete expression of an upper bound for the method is given based on the initial information. Also some properties of $S$-order of convergence and sufficient asymptotic error bound will be discussed.
Classification : 47H17, 47J25, 65H10, 65J15
Keywords: nonlinear operator equations; Banach spaces; Halley type method; Ostrowski-Kantorovich convergence theorem; Ostrowski-Kantorovich assumptions; optimal error \linebreak bound; $S$-order of convergence; sufficient asymptotic error bound 
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     author = {Chen, Dong},
     title = {Ostrowski-Kantorovich theorem and $S$-order of convergence of {Halley} method in {Banach} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {153--163},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {1993},
     mrnumber = {1240213},
     zbl = {0786.65051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a15/}
}
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Chen, Dong. Ostrowski-Kantorovich theorem and $S$-order of convergence of Halley method in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 153-163. http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a15/