the purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in banach spaces. our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).

In this paper, we prove the ∆-convergence theorems of the cyclic algorithm and the new multi-step iteration for k-strictly pseudo-contractive mappings and give also the strong convergence theorem of the modified Halpern’s iteration for these mappings in a CAT (0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature. Key–Words: CAT (0...

In this paper, we present a new semantics for the well-known normal system of modal logic K based on the notion of convergence spaces. The purpose is to use convergence spaces to model and reason about systems with both discrete and continuous states, so-called hybrid state spaces. K is sound and complete with respect to the class of convergence space models, and we show that Kripke frames and ...

We consider Wasserstein distance functionals for comparing between and assessing the convergence of latent discrete measures, which serve as mixing distributions in hierarchical and nonparametric mixture models. We explore the space of discrete probability measures metrized by Wasserstein distances, clarify the relationships between Wasserstein distances of mixing distributions and f -divergenc...

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity ...

We review notions of small sets,-irreducibility, etc., and present a simple proof of asymptotic convergence of general state space Markov chains to their stationary distributions.

A generalization of the cosine of the Friedrichs angle between two subspaces to several closed subspaces in a Hilbert space is given. This is used to analyze the rate of convergence in the von Neumann-Halperin method of cyclic alternating projections. General dichotomy theorems are proved, in the Hilbert or Banach space situation, providing conditions under which the alternative QUC/ASC (quick ...

Sufficient conditions have been given for the convergence in norm and a.e. of the ergodic Hilbert transform ([11], [5], [6]). Here we apply these conditions to the rotated ergodic Hilbert transform ∑ ∞ n=1 λ n n T f , where λ is a complex number of modulus 1. When T is a contraction in a Hilbert space, we show that the logarithmic Hausdorff dimension of the set of λ’s for which this series does...

An example of a D-metric space is given, in which D-metric convergence does not define a topology and in which a convergent sequence can have infinitely many limits. Certain methods for constructing D-metric spaces from a given metric space are developed and are used in constructing (1) an example of a D-metric space in which D-metric convergence defines a topology which is T1 but not Hausdorff...

The rate of H-convergence of truncations of stochastic infinite-dimensional systems du = [Au + B(u)]dt + G(u)dW, u(0, ·) = u0 ∈ H with nonrandom, local Lipschitz-continuous operators A,B and G acting on a separable Hilbert space H, where u = u(t, x) : [0, T ] × ID → IRd (ID ⊂ IRd) is studied. For this purpose, some new kind of monotonicity conditions on those operators and an existing H-series ...