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On the Local Convergence of Modified Homeier-Like Method in Banach Spaces

Authors
  • Panday, B.1
  • Jaiswal, J. P.2
  • 1 Regional Institute of Education, Department of Mathematics, Demonstration Multipurpose School, Bhopal, 462013, India , Bhopal (India)
  • 2 Maulana Azad National Institute of Technology, Department of Mathematics, Bhopal, 462003, India , Bhopal (India)
Type
Published Article
Journal
Numerical Analysis and Applications
Publisher
Pleiades Publishing
Publication Date
Oct 01, 2018
Volume
11
Issue
4
Pages
332–345
Identifiers
DOI: 10.1134/S1995423918040067
Source
Springer Nature
Keywords
License
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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 relax 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.

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