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Semilocal convergence on a family of root-finding multi-point methods in Banach spaces under relaxed continuity condition

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Abstract

In this paper, we consider the semilocal convergence on a family of root-finding multi-point methods. Compared with the results in reference (Hernández, M.A., Salanova, M.A., J. Comput. Appl. Math. 126, 131–143 3), these multi-point methods do not require the second derivative, Hölder continuity condition is relaxed, and the R-order is also enhanced. We prove an existence-uniqueness theorem of the solution. The R-order for these multi-point methods is at least 6 + q with relaxed continuous second derivative, where q∈[0,1].

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, 432000, Hubei, China

    Xiuhua Wang & Jisheng Kou

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  1. Xiuhua Wang
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  2. Jisheng Kou
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Correspondence to Jisheng Kou.

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Wang, X., Kou, J. Semilocal convergence on a family of root-finding multi-point methods in Banach spaces under relaxed continuity condition. Numer Algor 74, 643–657 (2017). https://doi.org/10.1007/s11075-016-0165-0

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