In this work, first, a family of fourth‐order methods is proposed to solve nonlinear equations.
The methods satisfy the Kung‐Traub optimality conjecture. By developing the methods into …

In this paper, some one-step iterative schemes with memory-accelerating methods are
proposed to update three critical values f′(r), f ″(r), and f‴(r) of a nonlinear equation f (x) …

The methods that use memory using accelerating parameters for computing multiple roots
are almost non-existent in the literature. Furthermore, the only paper available in this …

In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–
Halley's iterative technique to solve the nonlinear equation having the multiple roots. The …

In the paper, we iteratively solve a scalar nonlinear equation f (x)= 0, where f∈ C (I, R), x∈
I⊂ R, and I includes at least one real root r. Three novel two-step iterative schemes …

When exploring the literature, it can be observed that the operator obtained when applying
Newton-like root finding algorithms to the quadratic polynomials z 2− c has the same form …

Recently, self-accelerating technique has been widely used to improve the convergence
order of iterative methods for simple roots. However, it has not been applied in those for …

Here, we propose optimal fourth-order iterative methods for approximating multiple zeros of
univariate functions. The proposed family is composed of two stages and requires 3 …

In this paper we present an algorithm to obtain the parameter planes of families of root-
finding methods with several free critical points. The parameter planes show the joint …

In this manuscript, we introduce a two‐step convergent iterative scheme to compute the
roots with multiplicity mm of nonlinear equations. Most of the schemes in literature have …