Abstract: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.
Keywords: nonlinear operator equations, Banach spaces, Halley type method, Ostrowski-Kantorovich convergence theorem, Ostrowski-Kantorovich assumptions, optimal error bound, $S$-order of convergence, sufficient asymptotic error bound
AMS Subject Classification: 65H10, 65J15, 47H17