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

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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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Authors and Affiliations

  1. Department of Mathematics, Demonstration Multipurpose School, Regional Institute of Education, Bhopal, 462013, India

    B. Panday

  2. Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, 462003, India

    J. P. Jaiswal

Authors
  1. B. Panday
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  2. J. P. Jaiswal
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Correspondence to B. Panday.

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Original Russian Text © B. Panday, J.P. Jaiswal, 2018, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2018, Vol. 21, No. 4, pp. 419–433.

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Panday, B., Jaiswal, J.P. On the Local Convergence of Modified Homeier-Like Method in Banach Spaces. Numer. Analys. Appl. 11, 332–345 (2018). https://doi.org/10.1134/S1995423918040067

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