## 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 \(P\left( x\right) =0\)…

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

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

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

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

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…

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

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

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),\\…

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 \\…

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