The set of common fixed points of a oneparameter continuous semigroup of mappings is F(T(1)) cap F(T(sqrt 2))
Abstract
In this paper, we prove the following theorem: Let {T(t) : t >= 0} be a oneparameter continuous semigroup of mappings on a subset C of a Banach space E. The set of fixed points of T(t) is denoted by F(T(t)) for each t >= 0. Then cap_{t >= 0} F(T(t)) = F(T(1)) cap F(T(sqrt 2)) holds. Using this theorem, we discuss convergence theorems to a common fixed point of {T(t) : t >= 0}.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2004
 arXiv:
 arXiv:math/0408329
 Bibcode:
 2004math......8329S
 Keywords:

 Mathematics  Functional Analysis;
 47H20;
 47H10
 EPrint:
 10 pages