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## On some iterative methods for solving nonlinear operator equations

Abstract Let $$X,Y$$ be two Banach spaces and $$P:X\rightarrow Y$$ a nonlinear operator. For solving the equation $$P\left( x\right) =0$$…

## On some iterative methods for solving operator equations

Abstract Let $$X,Y$$ be two Banach spaces and $$P:X\rightarrow Y$$ a nonlinear operator. We study the semilocal convergence of the…

## Error estimation in the numerical solving of operator equations

Abstract Let $$X$$ be a Banach space and $$\varphi:X\rightarrow X$$ a nonlinear operator. Assume the equation $$x=\varphi \left( x\right)$$ has…

## Considerations regarding the iterative methods obtained by inverse interpolation

Abstract Let $$X,Y$$ be two normed spaces and $$P:X\rightarrow Y$$ a nonlinear operator. We consider the generalized inverse interpolation polynomial and…

## On iterated operators

Abstract Let $$X,Y$$ be normed spaces and $$F:X\rightarrow Y$$ a nonlinear operator. Let $$Q:X\rightarrow X.$$ We study the convergence orders of…

## On the iterative methods with high convergence orders

Abstract Let $$X$$ be a Banach space and $$Y$$ a normed space, and $$P:X\rightarrow Y$$ a nonlinear operator. In order…

## Interpolation in linear normed spaces and applications

Abstract Let $$X,Y$$ be two normed spaces and $$P:X\rightarrow Y$$ a nonlinear operator. We construct the Lagrange interpolation operator for…

## Solving the systems of operator equations by iterative methods

Abstract Let $$X,Y$$ be two Banach spaces and $$Z=X\times Y$$. We consider the system of nonlinear equations \[x=\varphi \left( x,y\right),\\…

## On interpolation with connected polynomials

Abstract We consider a function $$f\in C^{n-1}[a,b]$$ and the nodes $$a=x_{0}<x_{1}<\ldots<x_{m}=b$$. Given the values \begin{align}f\left( x_{i}\right) =&u_{i}, \quad i=1,…,m  \\…

## Remarks on solving the systems of equations by iterative methods

Abstract In this paper we give a condition for the convergence of an iterative method of Gauss-Seidel type  \[ x_i =…