Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
Convergence of iterates of Lasota-Mackey-Tyrcha operators
We provide sufficient and necessary conditions for asymptotic periodicity of iterates of strong Feller stochastic operators.
Convergence of iterates of linear operators and the Kelisky-Rivlin type theorems
Let X be a Banach space and T ∈ L(X), the space of all bounded linear operators on X. We give a list of necessary and sufficient conditions for the uniform stability of T, that is, for the convergence of the sequence of iterates of T in the uniform topology of L(X). In particular, T is uniformly stable iff for some p ∈ ℕ, the restriction of the pth iterate of T to the range of I-T is a Banach contraction. Our proof is elementary: It uses simple facts from linear algebra, and the Banach Contraction...
Convergence of iterates with errors of uniformly quasi-Lipschitzian mappings in cone metric spaces
Convergence of iterative algorithms to common random fixed points of random operators.
Convergence of iterative sequences for common zero points of a family of -accretive mappings in Banach spaces.
Convergence of iterative sequences for fixed point and variational inclusion problems.
Convergence of iterative sequences for generalized equilibrium problems involving inverse-strongly monotone mappings.
Convergence of Monotone Operators.
Convergence of moving averages of multiparameter superadditive processes.
Convergence of Newton-like methods for singular operator equations using outer inverses.
Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations is emphasized....
Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations...
Convergence of orthogonal series of projections in Banach spaces
For a sequence of mutually orthogonal projections in a Banach space, we discuss all possible limits of the sums in a “strong” sense. Those limits turn out to be some special idempotent operators (unbounded, in general). In the case of X = L₂(Ω,μ), an arbitrary unbounded closed and densely defined operator A in X may be the μ-almost sure limit of (i.e. μ-a.e. for all f ∈ (A)).
Convergence of paths for perturbed maximal monotone mappings in Hilbert spaces.
Convergence of the Ishikawa iterate for multi-valued mappings in metric spaces of hyperbolic type
Convergence of three-step iterations scheme for nonself asymptotically nonexpansive mappings.
Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings.
Convergence on composite iterative schemes for nonexpansive mappings in Banach spaces.
Convergence Rates for intermediate problems.