The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous iteration. However, it is possible to improve the accelerators. Therefore, we achieve superior convergence orders and obtain as hi...

* Correspondence: [email protected] Abdus Salam School of Mathematical Sciences, GC University, 68-b, New Muslim Town, Lahore 54600, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we extend some old and give some new refinements of the JensenSteffensen inequality. Further, we investigate the log-convexity and the exponential conve...

We provide suucient conditions for the convergence of Steeensen's method to a locally unique solution of a nonlinear operator equation on a Banach space. We use a xed point theorem and a special choice of divided diierences. Some applications of our results are also provided.

F R O M the results of experiments involving autoradiography of stretched H3 thymidine-labelled salivary gland chromosomes of Drosophila melanogaster, and a consideration of previously published evidence, STEFFENSEN (1963) has concluded that DNA (deoxyribonucleic acid) is absent from the interband regions of these chromosomes. In opposition to this conclusion are the results presented in this r...

We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [1], [5]-[28] using hypotheses up to the fifth derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius ...

It is attempted to present an efficient and free derivative class of Steffensen-like methods for solving nonlinear equations. To this end, firstly, we construct an optimal eighth-order three-step uniparameter without memory of iterative methods. Then the self-accelerator parameter is estimated using Newton's interpolation in such a way that it improves its convergence order from 8 to 12 without...