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...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

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...