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Semilocal Convergence of a Computationally Efficient Eighth-Order Method in Banach Spaces Under w-Continuity Condition

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Abstract

The current paper is concerned with the study of semilocal convergence of an eighth-order method for solving nonlinear equations in Banach spaces under mild condition. The existence and uniqueness theorem has been proved followed by the error estimates. At last, the application of theoretical development has been made in nonlinear integral equation.

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Acknowledgments

The author would like pay his gratitude to the reviewers for their valuable comments which play a key role in the improvement of this article. The author is also 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 (Ref. No. YSS/2015/001507).

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Authors and Affiliations

  1. Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, M.P., 462051, India

    J. P. Jaiswal

  2. Faculty of Science, Barkatullah University, Bhopal, M.P., 462026, India

    J. P. Jaiswal

  3. Regional Institute of Education, Bhopal, M.P., 462013, India

    J. P. Jaiswal

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  1. J. P. Jaiswal
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Correspondence to J. P. Jaiswal.

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Jaiswal, J.P. Semilocal Convergence of a Computationally Efficient Eighth-Order Method in Banach Spaces Under w-Continuity Condition. Iran J Sci Technol Trans Sci 42, 819–826 (2018). https://doi.org/10.1007/s40995-016-0115-7

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  • DOI: https://doi.org/10.1007/s40995-016-0115-7

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