## On the convergence order of the iterative methods

Abstract We study the connection between the convergence order of two sequences. We show that the exist sequences that do…

Abstract We study the connection between the convergence order of two sequences. We show that the exist sequences that do…

Abstract We consider a square matrix \(A\) with real or complex elements. We denote \(\mathbb{K}=\mathbb{R}\) or \(\mathbb{C}\) and we are…

Abstract In this paper we approach two aspects concerning the optimality problems arising from the consideration of the iterative methods for…

Abstract We extend the Steffensen method for solving the equation \(f\left( x\right)=0\) to the setting of the Banach spaces, \(f:X\rightarrow…

Abstract Let \(X_{1},X_{2}\) be two Banach spaces and \(f:X_{1}\rightarrow X_{2}\) a nonlinear equation. We study the chord method for solving…

Abstract Let \(X_{1},X_{2}\) be two Banach spaces, \(f:X_{1}\rightarrow X_{2}\) a nonlinear mapping. We study the convergence of the Steffensen method for…

Abstract Let \(X_{1},X_{2}\) be two Banach spaces, \(f:X_{1}\rightarrow X_{2}\) a nonlinear mapping and consider the chord method for solving the…

Abstract Let \(X\) be a Banach space, \(Y\) a normed space and the nonlinear operator equation \(P\left( x\right) =0\), where…

Abstract Let \(\left( X,\rho \right)\) be a complete metric space, \(f:X\rightarrow X\) a nonlinear mapping. In order to solve the…

Abstract Let \(\left( x_{i},\rho_{i}\right) ,\ i=1,2,\) be two complete metric space and \(F_{1}:X_{1}\times X_{2}\rightarrow X_{1},\ F_{2}:X_{1}\times X_{2}\rightarrow X_{2}\) two nonlinear…