Let { y”} be a trajectory defined sequentially by a nonlinear vector difference equation y,,+ 1 = F”+ ,( y,) with y0 known. A Steffensen-like iterative method is proposed which starts from a guessed sequence {u:‘)} for the approximation of { yn) and allows certain computations to be performed in parallel. The sequence {u:““‘} is (k) obtained from {u, } by means of a formula of the form u,+, (kt...

Building on the work of Josip Pečarić in 2013 and 1982 Srivastava 2017. We prove some new α-conformable dynamic inequalities Steffensen-type time scales. In case when α=1, we obtain well-known scale due to Steffensen inequalities. For specific scales, further show relevant as special cases: integral discrete Symmetry plays an essential role determining correct methods solve

In this paper, a family of Steffensen-type methods of optimal order of convergence with two parameters is constructed by direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub (J. Assoc. Comput. Math. 1974, 21, 634–651) that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2m−1. Furthermore, ...

Solving equations of the form H(x)=0 is one most faced problem in mathematics and other science fields such as chemistry or physics. This kind cannot be solved without use iterative methods. The Steffensen-type methods, defined using divided differences are derivative free, usually considered to solve these problems when H a non-differentiable operator due its accuracy efficiency. However, gene...