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A new convergence analysis for the two-step Newton method of order threeKeywords: Two-step Newton method , Newton's method , Banach space , Kantorovich hypothesis , majorizing sequence , Lipschitz/center-Lipschitz conditions Abstract: We present a tighter than before semilocal convergence analysis for the two-step Newton method of order three using recurrent functions. Numerical examples are also provided to show that our convergence criteria are satisfied but earlier studies such as in nine,thirteen,fifteen are not satisfied.
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