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

5 years ago

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

6 years ago

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

6 years ago

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

7 years ago

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

7 years ago

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

7 years ago

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

7 years ago

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

7 years ago

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

Fixed point theory

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