Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces.
Convergence of inexact iterative schemes for nonexpansive set-valued mappings.
Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point
Existence of fixed points of multivalued mappings that satisfy a certain contractive condition was proved by N. Mizoguchi and W. Takahashi. An alternative proof of this theorem was given by Peter Z. Daffer and H. Kaneko. In the present paper, we give a simple proof of that theorem. Also, we define Mann and Ishikawa iterates for a multivalued map with a fixed point and prove that these iterates converge to a fixed point of under certain conditions. This fixed point may be different from...
Convergence of Ishikawa iterates of generalized nonexpansive mappings.
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