Computational and Applied Mathematics

, Volume 37, Issue 4, pp 5082–5097 | Cite as

Extended Newton-type method for nonlinear functions with values in a cone

  • G. N. Silva
  • P. S. M. Santos
  • S. S. Souza


In this paper, we consider the problem of finding solutions of nonlinear inclusion problems in Banach space. Using convex optimization techniques introduced by Robinson (Numer Math 19:341–347, 1972), a convergence theorem for Kantorovich-like methods is given, which improves the results of Yamamoto (Jpn J Appl Math 3(2):295–313, 1986; Numer Math 51(5):545–557, 1987) and Robinson (Numer Math 19:341–347, 1972). The result is compared with previously known results. Numerical examples further justify the theoretical results.


Newton-like method Inclusion problem Banach space Convex process 

Mathematics Subject Classification

Primary 65K05 65K15 49M15 49M37 



The authors would like to thank the two anonymous referees for their constructive comments which have helped to substantially improve the presentation of the paper.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  1. 1.Centro das Ciências Exatas e das TecnologiasUniversidade Federal do Oeste da BahiaBarreirasBrazil
  2. 2.Departamento de Matemática, ParnaíbaUniversidade Federal do PiauíParnaíbaBrazil

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