Some fixed point results linked to α –β rational contractions and modified multivalued Hardy-Rogers operators
AbstractIn this paper two new fixed point results are studied. The first result is a theorem that involves (α −β)…
Nonlinear analysis
Approximating fixed points for nonlinear generalized mappings using Ishikawa iteration
AbstractWe obtain a contractive condition for the existence and uniqueness of fixed points for a generalized contraction-type mapping. The present…
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…
An application of the Picard operator technique to functional integral equations
Abstract In this paper we consider a functional integral equation of the form \[ x(t)=g(t,x(t),x(h(t)))+\int_{a}^{t} f(s,x(h(s)))ds+\int_{a}^{b} K(s,x(h(s)))ds, \ \ t…
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…