TITLE: Asymptotic Fixed Points, Part I.
ABSTRACT: By a standard exercise, a uniform contraction on a complete metric
space has a fixed point. Easy examples show that this fails if the
contraction is not uniform. I will discuss some recent results where the
uniform property is replaced by asymptotic conditions on the contraction.
These results are most easily framed and proved using methods from
nonstandard analysis, so I will also briefly brief review those methods. If
there is interest, I will actually prove some of the fixed-point results in
a second seminar (hence the “Part I.”)