On strong convergence by the hybrid method for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings.
On -stability of Picard iteration in cone metric spaces.
On the application of Newton's and chord methods of bifurcation problems.
On the approximation of some nonlinear equations.
On the blow-up phenomenon for the mass-critical focusing Hartree equation in ℝ⁴
We characterize the dynamics of the finite time blow-up solutions with minimal mass for the focusing mass-critical Hartree equation with H¹(ℝ⁴) data and L²(ℝ⁴) data, where we make use of the refined Gagliardo-Nirenberg inequality of convolution type and the profile decomposition. Moreover, we analyze the mass concentration phenomenon of such blow-up solutions.
On the Conley index in Hilbert spaces in the absence of uniqueness
Consider the ordinary differential equation (1) ẋ = Lx + K(x) on an infinite-dimensional Hilbert space E, where L is a bounded linear operator on E which is assumed to be strongly indefinite and K: E → E is a completely continuous but not necessarily locally Lipschitzian map. Given any isolating neighborhood N relative to equation (1) we define a Conley-type index of N. This index is based on Galerkin approximation of equation (1) by finite-dimensional ODEs and extends...
On the continuous dependence of the fixed points for -contractive-type operators
On the convergence and application of Stirling's method
We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.
On the convergence for an iterative method for quasivariational inclusions.
On the convergence of an implicit iterative process for generalized asymptotically quasi-nonexpansive mappings.
On the convergence of gelerkin approximations
On the convergence of implicit Ishikawa iterations with errors to a common fixed point of two mappings in convex metric spaces.
On the convergence of implicit iterative processes for asymptotically pseudocontractive mappings in the intermediate sense.
On the convergence of iterative sequences for a family of nonexpansive mappings and inverse-strongly monotone mappings.
On the convergence of Newton's method for analytic operators.
On the convergence of Newton's method under ω*-conditioned second derivative
We provide a new semilocal result for the quadratic convergence of Newton's method under ω*-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using ω-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.
On the convergence of perturbed Newton-like methods in Banach space and applications.
On the convergence of the Ishikawa iterates to a common fixed point of two mappings
Let be a convex subset of a complete convex metric space , and and be two selfmappings on . In this paper it is shown that if the sequence of Ishikawa iterations associated with and converges, then its limit point is the common fixed point of and . This result extends and generalizes the corresponding results of Naimpally and Singh [6], Rhoades [7] and Hicks and Kubicek [3].
On the convergence of the Ishikawa iteration in the class of quasi contractive operators.
On the convergence of the secant method under the gamma condition
We provide sufficient convergence conditions for the Secant method of approximating a locally unique solution of an operator equation in a Banach space. The main hypothesis is the gamma condition first introduced in [10] for the study of Newton’s method. Our sufficient convergence condition reduces to the one obtained in [10] for Newton’s method. A numerical example is also provided.