Colloquium

Thursday, Oct. 4, 2007

4:00 PM, BAC 219

Speaker: Barry Turett, Oakland University, Rochester, Michigan and Miami University, Oxford, Ohio
Distinguished Visiting Professor

Title: Some Recent (and not so recent) Results in Metric Fixed Point Theory

Abstract:

Consider a set C in a Banach space and a mapping T from the set C into itself.  What conditions do

you need to impose on C and T in order to ensure that T has a fixed point in C?  Questions of this

type have been intensively studied since 1912 when L.E.J. Brouwer proved his famous fixed point

theorem that continuous self-maps of compact, convex sets in finite-dimensional spaces have fixed

points.  In this talk, we consider progress on this question when C is a closed, bounded, convex

subsets of a Banach space and the mapping T is nonexpansive.