On a family of second-derivative-free variants of Chebyshev's method

In this paper, we present a family of new second-derivative-free variants of Chebyshev's method, in which f′(x) = 0 in some points is permitted. Analysis of convergence shows that the new methods are cubically convergent. Analysis of efficiency, in term of function evaluations, shows that the new methods have the great practical utility, which is demonstrated by numerical examples.