LOCAL CONVERGENCE OF INEXACT NEWTON-LIKE METHOD UNDER WEAK LIPSCHITZ CONDITIONS

doi:10.1007/s10473-020-0113-0

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (1): 199-210.doi: 10.1007/s10473-020-0113-0

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LOCAL CONVERGENCE OF INEXACT NEWTON-LIKE METHOD UNDER WEAK LIPSCHITZ CONDITIONS

Ioannis K. ARGYROS¹, Yeol Je CHO^2,3, Santhosh GEORGE⁴, Yibin XIAO²

1. Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA;
2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;
3. Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea;
4. Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, 757 025 India

Received:2018-10-19 Revised:2019-05-09 Online:2020-02-25 Published:2020-04-14
Contact: Yeol Je CHO E-mail:yjcho@gnu.ac.kr

Abstract

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

Key words: inexact Newton method, Banach space, semilocal convergence, weak and center-weak Lipschitz condition, recurrent functions, Kantorovich hypotheses

CLC Number:

65H10

Ioannis K. ARGYROS, Yeol Je CHO, Santhosh GEORGE, Yibin XIAO. LOCAL CONVERGENCE OF INEXACT NEWTON-LIKE METHOD UNDER WEAK LIPSCHITZ CONDITIONS[J].Acta mathematica scientia,Series B, 2020, 40(1): 199-210.

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References

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LOCAL CONVERGENCE OF INEXACT NEWTON-LIKE METHOD UNDER WEAK LIPSCHITZ CONDITIONS

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