✦ LIBER ✦

Iteration of maps by an automaton

✍ Scribed by F.M. Dekking

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 306 KB
Volume: 126
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90254-2

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✦ Synopsis

Let x=(x1, x2,. .) with the xi elements of a finite set A be an automatic sequence, i.e., x is generated by a tag machine with deletion number one. Let F be a finite set and suppose maps rp,: F+F are given for all aEA. It is shown constructively that the sequence of iterates (cp,,, cpx,ocpxl, cpx,"cpx,"cpx~."' ) is again an automatic sequence.

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## Abstract Let __E__ be a real reflexive Banach space having a weakly continuous duality mapping __J__~__φ__~ with a gauge function __φ__, and let __K__ be a nonempty closed convex subset of __E__. Suppose that __T__ is a non‐expansive mapping from __K__ into itself such that __F__ (__T__) ≠ ∅︁.