# (original)

## An algorithm in the solving of equations by interpolation

Abstract Consider the nonlinear equation in $$R$$, $$f\left( x\right) =0$$, where $$f:A\rightarrow B$$, $$(A,B\subseteq \mathbb{R})$$ which is assumed bijective. The Lagrange…

## Error estimations in the numerical solving of systems of equations in metric spaces

Abstract Let $$X_{1},X_{2}$$ be two complete metric spaces, $$X=X_{1}\times X_{2}$$ and the nonlinear mappings $$F_{1}:X\rightarrow X_{1},\ F_{2}:X\rightarrow X_{2}$$. In order…

## On the error estimation in the numerical convergence of certain iterative methods

Abstract We study the nonlinear equations of the form $x=\lambda D\left( x\right) +y,$ where $$\lambda \in \mathbb{R}$$ and $$y\in E$$…

## 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…

## On optimal iterative methods

Abstract Let $$\left( X,\rho \right)$$ be a complete matrix space, the nonlinear mapping $$\varphi:I\subset X\rightarrow X$$ and the equation \(x=\varphi…