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On the convergence of inexact Newton-like methods under mild differentiability conditions

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  • Singh, Vipin Kumar

Abstract

In the present paper, we have introduced an inexact Newton-like algorithm and discussed its semilocal convergence analysis under average Lipschitz condition as well as γ-Lipschitz condition for solving generalized operator equations containing non differentiable operators in Banach spaces. Our results extend and improve some well established results in the context of differentiability of involved operators. As special cases of our results, we re-obtain some well established results for the Newton method and inexact Newton method. We apply our result to solve Fredholm integral equations.

Suggested Citation

  • Singh, Vipin Kumar, 2020. "On the convergence of inexact Newton-like methods under mild differentiability conditions," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    • Handle: RePEc:eee:apmaco:v:370:y:2020:i:c:s009630031930863x
    DOI: 10.1016/j.amc.2019.124871
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    References listed on IDEAS

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    1. Daya Ram Sahu & Jen Chih Yao & Vipin Kumar Singh & Satyendra Kumar, 2017. "Semilocal Convergence Analysis of S-iteration Process of Newton–Kantorovich Like in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 102-127, January.
    2. Xiubin Xu & Yuan Xiao & Tao Liu, 2012. "Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, August.
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