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Convergence theorems of a new multiparametric family of Newton-like method in Banach space | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 335-362 اصل مقاله (512.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.17555.1948 | ||
| نویسندگان | ||
| Chandni Kumari؛ P K Parida* | ||
| Department of Mathematics, Central University of Jharkhand, Ranchi-835205, India | ||
| تاریخ دریافت: 20 فروردین 1398، تاریخ پذیرش: 07 مهر 1399 | ||
| چکیده | ||
| In this work, we have considered a new multi-parametric family of modified Newton-like methods(MNL) of order three to approximate a zero of a nonlinear operator in $\mathbb{B}$-space (Banach space). Here, we studied the semilocal convergence analysis of this family of methods by using a new type of majorant condition. Note that this majorant condition generalizes the earlier majorant conditions used for studying convergence analysis of third order methods. Moreover, by using second-order directional derivative of the majorizing function we obtained an error estimate. We also established relations between our majorant condition and assumption based on Kantorovich, Smale-type and Nesterov-Nemirovskii-type, that will show our result generalize these earlier convergence results. | ||
| کلیدواژه‌ها | ||
| Multi-parametric family of modified Newton-like (MNL) methods؛ Majorant conditions؛ Majorizing function؛ Nesterov-Nemirovskii condition؛ Kantorovich-type assumption؛ Smale-type assumption | ||
| مراجع | ||
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