## On the existence and uniqueness of positive solutions of some mildly nonlinear elliptic boundary value problems

AbstractFor a homogeneous Dirichlet problem attached to a semilinear elliptic equation we study the existence and uniqueness of non-negative solutions.…

## Estimating the radius of an attraction ball

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…

## 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,…

## Sufficient convergence conditions for certain accelerated successive approximations

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

## On the superlinear convergence of the successive approximations method

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

## On accelerating the convergence of the successive approximations method

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