Some variants of Ostrowskiʹs method with seventh-order convergence

In this paper, we present a class of new variants of Ostrowskiʹs method with order of convergence seven. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative and therefore this class of methods has the efficiency index equal to 1.627. Numerical tests verifying the theory are given, and multistep iterations, based on the present methods, are developed.