Abstract
In this paper, the semilocal convergence for a class of multi-point modified Chebyshev-Halley methods in Banach spaces is studied. Different from the results in reference [11], these methods are more general and the convergence conditions are also relaxed. We derive a system of recurrence relations for these methods and based on this, we prove a convergence theorem to show the existence-uniqueness of the solution. A priori error bounds is also given. The R-order of these methods is proved to be 5+q with ω−conditioned third-order Fréchet derivative, where ω(μ) is a non-decreasing continuous real function for μ > 0 and satisfies ω(0) ≥ 0, ω(tμ) ≤ t q ω(μ) for μ > 0,t ∈ [0,1] and q ∈ [0,1]. Finally, we give some numerical results to show our approach.
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Wang, X., Kou, J. Convergence for a class of multi-point modified Chebyshev-Halley methods under the relaxed conditions. Numer Algor 68, 569–583 (2015). https://doi.org/10.1007/s11075-014-9861-9
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DOI: https://doi.org/10.1007/s11075-014-9861-9