# Fixed point theory

## Sequences of contractions on cone metric spaces over Banach algebras and applications to nonlinear systems of equations and systems of differential equations

AbstractIt is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are…

## On the bifurcation of the null solutions of some mildly nonlinear elliptic boundary value problems

Abstract Existence and aymptotic expansion of some bifurcated solution for the following boundary value problem: \begin{align*} -\Delta u+cu^{2}-B^{2}u & =0,\ \…

## 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…