# nonlinear equations in Banach spaces

## 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,…

## 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 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…