On Convergence of the Accelerated Newton Method Under Generalized Lipschitz Conditions

M. Ya. Bartish and S. M. Shakhno, “On the Newton method with accelerated convergence,” Vestn. Kiev. Univ., Modelir. Optimiz. Slozhn. Sistem, No. 6, 62–66 (1987). M. Ya. Bartish and S. M. Shakhno, On a Class of Newton-Type Iterative Methods [in Russian], Deposited at UkrNIINTI 17.09.87, No. 2580-Uk87, Lviv (1987). L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1984). J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic, New York (1970). S. M. Shakhno, “Convergence of inexact difference methods under the generalized Lipschitz conditions,” Mat. Metody Fiz.-Mekh. Polya, 52, No. 3, 30–40 (2009); English translation: J. Math. Sci., 171, No. 4, 453–465 (2010). S. M. Shakhno, “Steffensen method under generalized Lipschitz conditions for the first-order divided differences,” Mat. Stud., 31, No. 1, 90–95 (2009). S. M. Shakhno, Investigation of Convergence of the Accelerated Newton Method [in Russian], Deposited at UkrNIINTI 17.09.87, No. 2579-Uk87, Lviv (1987). J. Chen and W. Li, “Convergence behavior of inexact Newton methods under weak Lipschitz condition,” J. Comput. Appl. Math., 191, No. 1, 143–164 (2006). S. M. Shakhno, “On the secant method under generalized Lipschitz conditions for the divided difference operator,” Proc. Appl. Math. Mech., 7, No. 1, 2060083–2060084 (2007). X. Wang, “Convergence of Newton’s method and uniqueness of the solution of equations in Banach space,” IMA, J. Numer. Anal., 20, No. 1, 123–134 (2000). W. Werner, “Newton-like methods for the computation of fixed points,” Comput. & Math. Appl., 10, No. 1, 77–86 (1984). W. Werner, “Über ein Verfahren der Ordnung \( 1+\sqrt{2} \) zur Nullstellenbestimmung,“ Numer. Math., 32, No. 3, 333–342 (1979).