On the convergence of open Newton’s method

Abstract

Cordero and Torregrosa proved the convergence of two Newton’s-like methods in 2007. Using Taylor expansion (requiring existence of derivatives of order up to four of the involved operator) they obtained the convergence order three for these methods. The convergence order three is obtained for Open Newton’s method and two extensions of it with assumptions only on first two derivatives of the operator involved. We verified the results with examples and dynamics of the results are presented. © 2023, The Author(s), under exclusive licence to The Forum D’Analystes.