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    Ball convergence of a sixth-order Newton-like method based on means under weak conditions

    Autor: 
    Magreñán, Á. Alberto (1)
    ;
    Argyros, Ioannis K
    ;
    Rainer, J Javier (1)
    ;
    Sicilia, Juan Antonio (1)
    Fecha: 
    08/2018
    Palabra clave: 
    Newton-like method; local convergence; stolarky means; gini means; efficiency index; Scopus; JCR
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/6653
    DOI: 
    https://doi.org/10.1007/s10910-018-0856-y
    Dirección web: 
    https://link.springer.com/article/10.1007/s10910-018-0856-y
    Resumen:
    We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative or even higher. The convergence in this study is shown under hypotheses on the first derivative although only the first derivative appears in these methods. Hence, the applicability of the method is expanded. Finally, we solve the problem of the fractional conversion in the ammonia process showing the applicability of the theoretical results.
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