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
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.
 Dong Chen: On a New Definition of Order of Convergence in General Iterative Methods I: One Point Iterations. Research Report No. 7, Department of Mathematical Sciences, University of Arkansas, 1991.
 Dong Chen: On a New Definition of Order of Convergence in General Iterative Methods II: Multipoint Iterations. Research Report No. 8, Department of Mathematical Sciences, University of Arkansas, 1991.
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