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Local Convergence of Inexact Newton-Like Method under Weak Lipschitz Conditions

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Abstract

The paper develops the local convergence of Inexact Newton-Like Method (INLM) for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The obtained results compare favorably with earlier ones such as [7, 13, 14, 18, 19]. A numerical example is also provided.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Yeol Je Cho

  3. Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Karnataka, 757 025, India

    Santhosh George

  4. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea

    Yeol Je Cho & Yibin Xiao  (肖义彬)

Authors
  1. Ioannis K. Argyros
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  2. Yeol Je Cho
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  3. Santhosh George
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  4. Yibin Xiao  (肖义彬)
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Correspondence to Yeol Je Cho.

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Argyros, I.K., Cho, Y.J., George, S. et al. Local Convergence of Inexact Newton-Like Method under Weak Lipschitz Conditions. Acta Math Sci 40, 199–210 (2020). https://doi.org/10.1007/s10473-020-0113-0

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  • DOI: https://doi.org/10.1007/s10473-020-0113-0

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