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Analyzing the semilocal convergence of a fourth-order Newton-type scheme with novel majorant and average Lipschitz conditions
J. P. Jaiswalabc a Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, C.G., India-495009
b Faculty of Science, Barkatullah University, Bhopal, M.P., India-462026
c Regional Institute of Education, Bhopal, M.P., India-462013
Abstract:
The main focus of this paper is an analysis of the semilocal convergence (S.C.) of a three-step Newton-type scheme (TSNTS) used for finding the solution of nonlinear operators in Banach spaces (B.S.). A novel S.C. analysis of the TSNTS is introduced, which is based on the assumption that a generalized Lipschitz condition (G.L.C.) is satisfied by the first derivative of the operator.
The findings contribute to the theoretical understanding of TSNTS in B.S. and have practical implications in various applications, such as integral equations further validating our results.
Key words:
semilocal convergence, nonlinear problem, convergence radius, Banach space, generalized Lipschitz condition, $\varkappa$-average.
Received: 30.08.2023 Revised: 20.10.2023 Accepted: 27.10.2023
Citation:
J. P. Jaiswal, “Analyzing the semilocal convergence of a fourth-order Newton-type scheme with novel majorant and average Lipschitz conditions”, Sib. Zh. Vychisl. Mat., 27:1 (2024), 11–32
Linking options:
https://www.mathnet.ru/eng/sjvm858 https://www.mathnet.ru/eng/sjvm/v27/i1/p11
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Abstract page: | 26 | Full-text PDF : | 2 | References: | 5 | First page: | 2 |
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