-error analysis for a system of quasivariational inequalities with noncoercive operators.
Landesman-Lazer-Alternative Theorems for a Class of Nonlinear Functional Equations.
Le equazioni funzionali in analisi non lineare
Lie generators for one parameter semigroups of transformations.
Limit sets in product of semi-dynamical systems.
Limits of Sequences of Operators on Spaces of Vector Valued Functions.
Linear complementarity problem and extremal hyperplanes
Local and semilocal convergence theorems for Newton's method based on continuously Fréchet differentiable operators.
Local asymptotic stability for nonlinear quadratic functional integral equations.
Local convergence analysis for a certain class of inexact methods.
Local convergence analysis of inexact Newton-like methods.
Local convergence for a family of iterative methods based on decomposition techniques
We present a local convergence analysis for a family of iterative methods obtained by using decomposition techniques. The convergence of these methods was shown before using hypotheses on up to the seventh derivative although only the first derivative appears in these methods. In the present study we expand the applicability of these methods by showing convergence using only the first derivative. Moreover we present a radius of convergence and computable error bounds based only on Lipschitz constants....
Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions
We present a local multi-point convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided.
Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative
We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That is why we consider inexact Newton methods, where the Newton equations are solved only approximately, and in some unspecified manner. In earlier works [2], [3], natural assumptions under which the forcing sequences are uniformly less than one were given based on the second Fréchet derivative of the operator...
Local convergence of two competing third order methods in Banach space
We present a local convergence analysis for two popular third order methods of approximating a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for both methods under the same conditions. A comparison is given between the two methods, as well as numerical examples.
Local convergence theorems for Newton's method from data at one point
We provide local convergence theorems for the convergence of Newton's method to a solution of an equation in a Banach space utilizing only information at one point. It turns out that for analytic operators the convergence radius for Newton's method is enlarged compared with earlier results. A numerical example is also provided that compares our results favorably with earlier ones.
Local convergence theorems of Newton’s method for nonlinear equations using outer or generalized inverses
We provide local convergence theorems for Newton’s method in Banach space using outer or generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Fréchet-derivative. This way our convergence balls differ from earlier ones. In fact we show that with a simple numerical example that our convergence ball contains earlier ones. This way we have a wider choice of initial guesses than before. Our results can be used to solve undetermined systems, nonlinear...
Local Lipschitz continuity of the stop operator
On a closed convex set in with sufficiently smooth () boundary, the stop operator is locally Lipschitz continuous from into . The smoothness of the boundary is essential: A counterexample shows that -smoothness is not sufficient.
Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point
In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R k →Y is a C 2-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R 1 that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ0)∈X×R k and we describe the solution set of the studied equation in a small neighbourhood of this point.
Local structure of the zero-sets of differentiable mappings and application to bifurcation theory.