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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.22 no.1 Temuco Apr. 2020 


Super-Halley method under majorant conditions in Banach spaces

Shwet Nisha1 

P. K. Parida2 

1Department of Applied Mathematics, Central University of Jharkhand, Ranchi-835205, India.

2Department of Applied Mathematics, Central University of Jharkhand, Ranchi-835205, India.


In this paper, we have studied local convergence of Super-Halley method in Banach spaces under the assumption of second order majorant conditions. This approach allows us to obtain generalization of earlier convergence analysis under majorizing sequences. Two important special cases of the convergence analysis based on the premises of Kantorovich and Smale type conditions have also been concluded. To show efficacy of our approach we have given three numerical examples.

Keywords and Phrases: Nonlinear equations; Super-Halley method; Majorant conditions; Local Convergence; Semilocal Convergnce; Smale-type conditions; Kantorovich-type conditions


En este artículo, hemos estudiado la convergencia local del método Super-Halley en espacios de Banach, asumiendo condiciones mayorantes de segundo orden. Este punto de vista nos permite obtener generalizaciones de análisis de convergencia bajo sucesiones mayorantes obtenidos anteriormente. También se han concluido dos casos especiales del análisis de convergencia basados en las premisas de condiciones tipo Kantorovich y Smale. Para mostrar la eficacia de nuestro enfoque, damos tres ejemplos numéricos.

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