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Extending the applicability of high-order iterative schemes under Kantorovich hypotheses and restricted convergence regions

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Abstract

We use restricted convergence regions to locate a more precise set than in earlier works containing the iterates of some high-order iterative schemes involving Banach space valued operators. This way the Lipschitz conditions involve tighter constants than before leading to weaker sufficient semilocal convergence criteria, tighter bounds on the error distances and an at least as precise information on the location of the solution. These improvements are obtained under the same computational effort since computing the old Lipschitz constants also requires the computation of the new constants as special cases. The same technique can be used to extend the applicability of other iterative schemes. Numerical examples further validate the new results.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Department of Mathematical and Computational Sciences, NIT Karnataka, Mangalore, 575 025, India

    Santhosh George

  3. Department of Mathematics, Manipal Institute of Technology, Manipal, Karnataka, 576104, India

    Shobha M. Erappa

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  1. Ioannis K. Argyros
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  2. Santhosh George
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  3. Shobha M. Erappa
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Correspondence to Shobha M. Erappa.

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Argyros, I.K., George, S. & Erappa, S.M. Extending the applicability of high-order iterative schemes under Kantorovich hypotheses and restricted convergence regions. Rend. Circ. Mat. Palermo, II. Ser 69, 1107–1113 (2020). https://doi.org/10.1007/s12215-019-00460-x

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