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

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 ??conditioned third-order Frechet derivative, where ?(μ) is a non-decreasing continuous real function for μ > 0 and satisfies ?(0) ? 0, ?(tμ) ≤ t q ?(μ) for μ > 0,t ? [0,1] and q ? [0,1]. Finally, we give some numerical results to show our approach.