Implicit and explicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings.
Implicit approximation methods for common fixed points of a finite family of strictly pseudocontractive mappings in Banach spaces
Implicit iteration methods with errors for discrete non-Lipschitzian families with perturbed mappings.
Implicit iteration process for common fixed points of strictly asymptotically pseudocontractive mappings in Banach spaces.
Implicit iteration process of nonexpansive non-self-mappings.
Implicit variational-like inclusions involving general -monotone operators.
Improved ball convergence of Newton's method under general conditions
We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of...
Improved estimates for the Ginzburg-Landau equation : the elliptic case
We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the -energy and the parameter . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.
Impulsive boundary value problems for -Laplacian’s via critical point theory
In this paper we investigate the existence of solutions to impulsive problems with a -Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence...
Inclusion Statements for Operator Equations by a Continuity Principle.
Inégalités variationnelles non convexes
Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d’inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée.
Inertial forward-backward splitting method in Banach spaces with application to compressed sensing
We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.
Inexact Newton method under weak and center-weak Lipschitz conditions
The paper develops semilocal convergence of Inexact Newton Method INM for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The results obtained compare favorably with earlier ones in at least the case of Newton's Method (NM). Numerical examples, where our convergence criteria are satisfied but the earlier ones are not, are also explored.
Inexact Newton methods and recurrent functions
We provide a semilocal convergence analysis for approximating a solution of an equation in a Banach space setting using an inexact Newton method. By using recurrent functions, we provide under the same or weaker hypotheses: finer error bounds on the distances involved, and an at least as precise information on the location of the solution as in earlier papers. Moreover, if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained. Furthermore, numerical...
Infinite dimensional non-symmetric Borsuk-Ulam theorem
Infinitely many positive solutions for the Neumann problem involving the p-Laplacian
We present two results on existence of infinitely many positive solutions to the Neumann problem ⎧ in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, with and f: Ω × ℝ → ℝ is a Carathéodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.
Infinitely many solutions for a semilinear elliptic equation in via a perturbation method
We introduce a method to treat a semilinear elliptic equation in (see equation (1) below). This method is of a perturbative nature. It permits us to skip the problem of lack of compactness of but requires an oscillatory behavior of the potential b.
Infinitely many solutions of a second-order -Laplacian problem with impulsive condition
Using the critical point theory and the method of lower and upper solutions, we present a new approach to obtain the existence of solutions to a -Laplacian impulsive problem. As applications, we get unbounded sequences of solutions and sequences of arbitrarily small positive solutions of the -Laplacian impulsive problem.
Inflated mappings for singularities of codimension
Injectivity onto a star-shaped set for local homeomorphisms in n-space
We provide a number of either necessary and sufficient or only sufficient conditions on a local homeomorphism defined on an open, connected subset of the n-space to be actually a homeomorphism onto a star-shaped set. The unifying idea is the existence of "auxiliary" scalar functions that enjoy special behaviours along the paths that result from lifting the half-lines that radiate from a point in the codomain space. In our main result this special behaviour is monotonicity, and the auxiliary function...