Argyros, Ioannis K.; Ren, Hongmin A simplified proof of the Kantorovich theorem for solving equations using telescopic series. (English) Zbl 1399.65120 J. Numer. Anal. Approx. Theory 44, No. 2, 146-153 (2015). Summary: We extend the applicability of the Kantorovich theorem (KT) for solving nonlinear equations using Newton-Kantorovich method in a Banach space setting. Under the same information but using elementary scalar telescopic majorizing series, we provide a simpler proof for the (KT) I. Argyros [Studies in Computational Mathematics 15. Amsterdam: Elsevier, xv, 487 p. (2007; Zbl 1147.65313)]; L. V. Kantorovich and G. P. Akilov [Oxford etc.: Pergamon Press. XIV, 589 p. (1982; Zbl 0484.46003)]. Our results provide at least as precise information on the location of the solution. Numerical examples are also provided in this study. MSC: 65J15 Numerical solutions to equations with nonlinear operators 65G99 Error analysis and interval analysis 47H99 Nonlinear operators and their properties 49M15 Newton-type methods Keywords:Newton-Kantorovich method; Banach space; majorizing series; telescopic series; Kantorovich theorem Citations:Zbl 1147.65313; Zbl 0484.46003 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{H. Ren}, J. Numer. Anal. Approx. Theory 44, No. 2, 146--153 (2015; Zbl 1399.65120)