A variant of the Newton method
Abstract Let \(X\) be a Banach space, \(Y\) a normed space, \(P:X\rightarrow Y\) a nonlinear operator and the equation \(P\left(…
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On the approximation of the solutions of equations in Banach spaces by sequences
Abstract Let \(X\) be a Banach space, \(Y\) a normed space \(P:X\rightarrow Y\) a nonlinear operator and the equation \(P\left(…
On the convergence of a class of iteration methods of J. F. Traub
Abstract Let \(X\) be a Banach space, \(Y\) a normed space and \(P:X\rightarrow Y\) a nonlinear operator. We study the…
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…