Local convergence of an at least sixth-order method in Banach spaces

  • I. K. Argyros
  • S. K. Khattri
  • S. GeorgeEmail author


We present a local convergence analysis of an at least sixth-order family of methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. The semilocal convergence analysis of this method was studied by Amat et al. in (Appl Math Comput 206:164–174, 2008; Appl Numer Math 62:833–841, 2012). This work provides computable convergence ball and computable error bounds. Numerical examples are also provided in this study.


Sixth-order methods three-step Newton-like methods Banach space local convergence majorizing sequences recurrent relations recurrent functions 

Mathematics Subject Classification

65H10 65G99 65K10 47H17 49M15 



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Authors and Affiliations

  1. 1.Department of Mathematical SciencesCameron UniversityLawtonUSA
  2. 2.Department of EngineeringStord Haugesund University CollegeHaugesundNorway
  3. 3.Department of Mathematical and Computational SciencesNational Institute of Technology KarnatakaMangaluruIndia

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