Weak convergence and spectrality of infinite convolutions

Convergence of trajectories in infinite horizon optimization

In this paper, we investigate the convergence of a sequence of minimizing trajectories in infinite horizon optimization problems. The convergence is considered in the sense of ideals and their particular case called the statistical convergence. The optimality is defined as a total cost over the infinite horizon.

Weak Convergence and Weak* Convergence1

In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By...

Image Measures of Infinite Product Measures and Generalized Bernoulli Convolutions

We examine measure preserving mappings f acting from a probability space (Ω, F, μ) into a probability space (Ω, F , μ) , where μ = μ(f−1). Conditions on f , under which f preserves the relations ”to be singular” and ”to be absolutely continuous” between measures defined on (Ω, F ) and corresponding image measures, are investigated. We apply the results to investigate the distribution of the ran...

Weak Convergence of Mann Iterative Algorithm for two Nonexpansive mappings

The mann fixed point algorithm play an importmant role in the approximation of fixed points of nonexpansive operators. In this paper, by considering new conditions, we prove the weak convergence of mann fixed point algorithm, for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces. This results extend the privious results given by Kanzow and Shehu. Finally, we give ...

Strong and Weak Convergence Theorems for an Infinite Family of Lipschitzian Pseudocontraction Mappings in Banach Spaces