On the convergence of some quasi-Newton iterates studied by I. Păvăloiu
Abstract In 1986, I. Păvăloiu [6] has considered a Banach space and the fixed point problem \[x=\lambda D\left( x\right) +y,…
nonlinear equations in Banach spaces
On a third order iterative method for solving polynomial operator equations
Abstract We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree (2).…
On the Steffensen method for solving nonlinear operator equations
Abstract We consider the equation F\left( x\right) =x-A\left( x\right)=0, where A is an operator from a Banach space X to…
On some Steffensen-type iterative methods for a class of nonlinear equations
Abstract Consider the nonlinear equations H(x):=F(x)+G(x)=0, with F differentiable and G continuous, where F,G,H:X \rightarrow X are nonlinear operators and X…
On some iterative methods for solving nonlinear equations
Abstract Consider the nonlinear equation H(x):=F(x)+G(x)=0, with F differentiable and G continuous, where F,G,H:X \rightarrow X, X a Banach space. The…
On some interpolatory iterative methods for the second degree polynomial operators (I)
Abstract In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree…
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…
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…