On the structure of fixed-point sets of asymptotically regular semigroups

Details On the structure of fixed-point sets of asymptotically regular semigroups On the structure of fixed-point sets of asymptotically regular semigroups

2012-01-04

arxiv.org/abs/1201.0986v1

Mathematics

Functional Analysis

11 pages

Scientific paper

We extend a few recent results of G\'{o}rnicki (2011) asserting that the set
of fixed points of an asymptotically regular mapping is a retract of its
domain. In particular, we prove that in some cases the resulting retraction is
H\"{o}lder continuous. We also characterise Bynum's coefficients and the Opial
modulus in terms of nets.

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