From a dynamical point of view applied to complex polynomials, we study a number of root–finding iterative methods. We consider Newton’s method, Newton’s method for multiple roots, Jarratt’s method, the super–Halley method, the convex as well as the double convex acceleration of Whittaker’s method, the methods of Chebyshev, Stirling, and Steffensen, among others. Since all of the iterative root...

In this paper, seven self-accelerating iterative methods with memory are derived from an optimal two-step Steffensen-type method without memory for solving nonlinear equations, their orders of convergence are proved to be increased from 4 to 2 6 , (5 17) / 2 ,5 and (5 33) / 2 , numerical examples are demonstrat-ed demonstrated to verify the theoretical results, and applications for solving syst...

In order to reduce localization error of the sensor node, a novel node localization algorithm (DVHop-Steff) is proposed in this paper based on DV-Hop algorithm and Steffensen iterative method. Firstly, DV-Hop algorithm is used to obtain location position of wireless sensor nodes; and then Steffensen iterative method is used to correct the locate results of DV-Hop algorithm and achieve higher lo...

We further present a new modification to the quadratically convergent iteration formulae proposed by Mamta et al. [Mamta, V. Kanwar, V.K. Kukreja, S. Singh, On a class of quadratically convergent iteration formulae, Appl. Math. Comput. 166 (2005) 633–637] for solving single variable nonlinear equations. It is proven that the modification converges cubically. Further, a new family with cubic con...

Steffensen-type methods are practical in solving nonlinear equations. Since, such schemes do not need derivative evaluation per iteration. Hence, this work contributes two new multistep classes of Steffensen-type methods for finding the solution of the nonlinear equation f x 0. New techniques can be taken into account as the generalizations of the one-step method of Steffensen. Theoretical proo...

We consider the Steffensen–Hayashi inequality and remainder identity for V-fractional differentiable functions involving six parameters truncated Mittag–Leffler function Gamma function. In view of these, we obtain some integral inequalities Steffensen, Hermite–Hadamard, Chebyshev, Ostrowski, Grüss type to calculus.

Jensen–Steffensen type inequalities for P -convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen–Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.