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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2018, Volume 21, Number 4, Pages 419–433
DOI: https://doi.org/10.15372/SJNM20180406 (Mi sjvm694) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the local convergence of modified Homeier-like method in Banach spaces

B. Pandaya, J. P. Jaiswalb

a Department of Mathematics, Demonstration Multipurpose School, Regional Institute of Education, Bhopal, 462013 India
b Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, 462003 India
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DOI: https://doi.org/10.15372/SJNM20180406
Abstract: The aim of this article is to investigate the local convergence analysis of the multi-step Homeier-like approach in order to approximate the solution of nonlinear equations in Banach spaces, which fulfilled the Lipschitz as well as Hölder continuity condition. The Hölder condition is more relaxer than Lipschitz condition. Also, the existence and uniqueness theorem has been derived and found their error bounds. Numerical examples are available to appear the importance of theoretical discussions.
Key words: Banach space, local convergence, nonlinear equation, Lipschitz condition, Hölder condition.
Funding agency Grant number
Science and Engineering Research Board YSS/2015/001507
The last author is thankful to Science and Engineering Research Board (New Delhi, India) for approving the research project under the scheme Start Up Research Grant for Young Scientists (grant no. YSS/2015/001507).
Received: 05.07.2017
Revised: 05.02.2018
English version:
Numerical Analysis and Applications, 2018, Volume 11, Issue 4, Pages 332–345
DOI: https://doi.org/10.1134/S1995423918040067
Bibliographic databases:
Document Type: Article
MSC: 65D10, 65D99, 65G99, 90C30
Language: Russian
Citation: B. Panday, J. P. Jaiswal, “On the local convergence of modified Homeier-like method in Banach spaces”, Sib. Zh. Vychisl. Mat., 21:4 (2018), 419–433; Num. Anal. Appl., 11:4 (2018), 332–345
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
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