Abstract
The principal objective of this study is to propose two derivative free iteration functions. Both are applicable to each earlier optimal multi-point derivative free scheme of order four and eight whose first sub step should be Steffensen's type method to develop more advanced optimal iteration techniques of order eight and sixteen, respectively. Both schemes satisfy the Kung-Traub optimality conjecture. In addition, the theoretical convergence properties of our schemes are fully explore with the help of main theorem that demonstrate the convergence order. The performance and effectiveness of our optimal iteration functions have compared with the existing competitors on some standard academic problems. Finally, on the account of results obtained, our methods are find to be more efficient as compared to some standard and robust iteration functions of same order.