Convergence for a class of multi-point modified Chebyshev-Halley methods under the relaxed conditions.

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 ω( μ) for μ > 0, t ∈ [0,1] and q ∈ [0,1]. Finally, we give some numerical results to show our approach. [ABSTRACT FROM AUTHOR]