## A generalization of the Newton method

Abstract Let $$X$$ be a Banach space, $$Y$$ a normed space, $$G:X\rightarrow Y$$ a nonlinear operator, and $$G\left( x\right) =0$$…

## Solving equations with the aid of inverse rational interpolation functions

Abstract We study the convergence of an iterative method for solving the equation $$f\left( x\right) =0,\ f:A\rightarrow B$$, $$A,B\subseteq \mathbb{R}$$, $$f$$…

## Solving equations by Hermite type inverse interpolation

Abstract We study the convergence of an iterative method for solving the equation (fleft( xright) =0, f:Isubseteq mathbb{Rrightarrow R}). The…

## Solving equations with the aid of inverse interpolation spline functions

Abstract We consider the solving of a nonlinear equation in $$\mathbb{R}$$. We construct a spline function which approximates the nonlinear…

## Optimal Steffensen type iterative methods obtained by inverse interpolation

Abstract Let $$f:I\subset \mathbb{R\rightarrow R}$$ be a nonlinear mapping and the equation $$f\left( x\right) =0$$ with solution $$x^{\ast}$$; consider the…