Geodesic
Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 3, pp. 289-300.

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We present a local convergence analysis of a one parameter Jarratt-type method. We use this method to approximate a solution of an equation in a Banach space setting. The semilocal convergence of this method was recently carried out in earlier studies under stronger hypotheses. Numerical examples are given where earlier results such as in [Ezquerro J.A., Hernández M.A., {New iterations of $R$-order four with reduced computational cost}, BIT Numer. Math. {49} (2009), 325--342] cannot be used to solve equations but our results can be applied.
DOI : 10.14712/1213-7243.2015.171
Classification : 65D10, 65D99
Keywords: Banach space; Newton's method; local convergence; radius of convergence 
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Argyros, I. K.; González, D.; Khattri, S. K. Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 3, pp. 289-300. doi : 10.14712/1213-7243.2015.171. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.171/

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