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

Authors
  • Argyros, Ioannis K.1
  • Cho, Yeol Je2, 3
  • George, Santhosh4
  • Xiao, Yibin3
  • 1 Cameron University, Lawton, OK, 73505, USA , Lawton (United States)
  • 2 University of Electronic Science and Technology of China, Chengdu, 611731, China , Chengdu (China)
  • 3 Gyeongsang National University, Jinju, 52828, Korea , Jinju (South Korea)
  • 4 National Institute of Technology Karnataka, Karnataka, 757 025, India , Karnataka (India)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Dec 17, 2019
Volume
40
Issue
1
Pages
199–210
Identifiers
DOI: 10.1007/s10473-020-0113-0
Source
Springer Nature
Keywords
License
Yellow

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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