Speaker
Prof.
Eva Kopecka
(Universität Innsbruck)
Description
Let $C_1, \dots, C_K$ be closed, convex and quasi-symmetric subsets of a Hilbert space $H$ with a nonempty intersection $C=\bigcap_1^K C_j$.
A sequence of indices $\alpha\in \{1,\dots,K\}^{\mathbb N}$ and $x_0\in H$ generate the sequence of projections
$$
x_{n+1}=P_{\alpha(n)}x_n, \qquad n=0,1,2,\dots;
$$
here $P_{\alpha(n)}$ denotes the nearest point projection onto the convex set $C_{\alpha(n)}$.
We show that for almost all sequences $\alpha$ of indices the generated sequence of projections converges to a point in $C$.
Affiliation
Institut für Mathematik
Universität Innsbruck
Author
Prof.
Eva Kopecka
(Universität Innsbruck)