## Perturbed-Steffensen-Aitken projection methods for solving equations with nondifferentiable operators

Abstract We use perturbed Steffensen-Aitken methods to approximate a locally unique solution of an operator equation in a Banach space. Using…

Abstract We use perturbed Steffensen-Aitken methods to approximate a locally unique solution of an operator equation in a Banach space. Using…

Abstract We use inexact Steffensen-Aitken-type methods to approximate implicit functions in a Banach space. Using a projection operator our equation reduces to…

Abstract Given a nonlinear mapping \(G:D\subseteq \mathbb{R}^n\rightarrow \mathbb{R}^n\) differentiable at a fixed point \(x^\ast\), the Ostrowski theorem offers the sharp…

Abstract In 1986, I. Păvăloiu [6] has considered a Banach space and the fixed point problem \[x=\lambda D\left( x\right) +y,…

Abstract A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method,…

Abstract We have recently characterized the q-quadratic convergence of the perturbed successive approximations. For a particular choice of the parameters, these…

Abstract The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 = G(xk) near a fixed…

Abstract The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…

Abstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…

Abstract No q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when…