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

Vipin Kumar Singh

Applied Mathematics and Computation, 2020, vol. 370, issue C

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.

Keywords: Nonlinear operator equation; Fréchet derivative; Newton–Kantorovich method; Inexact newton’s method and fredholm integral equation (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:370:y:2020:i:c:s009630031930863x

DOI: 10.1016/j.amc.2019.124871

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