Numerical Analysis and Applications

, Volume 11, Issue 4, pp 332–345 | Cite as

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

  • B. PandayEmail author
  • J. P. Jaiswal


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.


Banach space local convergence nonlinear equation Lipschitz condition Hölder condition 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Demonstration Multipurpose SchoolRegional Institute of EducationBhopalIndia
  2. 2.Department of MathematicsMaulana Azad National Institute of TechnologyBhopalIndia

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