 CARMA SEMINAR
 Speaker: Wojciech Kozlowski, University of NSW
 Title: Common fixed points for semigroups of pointwise Lipschitzian mappings in Banach spaces
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 2:00 pm, Fri, 22^{nd} Jul 2011
 Abstract:
We will investigate the existence of common fixed points for pointwise Lipschitzian semigroups of nonlinear mappings $Tt : C  C$ where $C$ is a bounded, closed, convex subset of a uniformly convex Banach space $X$, i.e. a family such that $T0(x) = x$, $Ts+t = Ts(Tt(x))$, where each $Tt$ is pointwise Lipschitzian, i.e. there exists a family of functions $at : C  [0;x)$ such that $Tt(x)Tt(y) < at(x)xy$ for $x$, $y \in C$. We will also demonstrate how the asymptotic aspect of the pointwise Lipschitzian semigroups can be expressed in terms of the respective Frechet derivatives. We will discuss some questions related to the weak and strong convergence of certain iterative algorithms for the construction of the stationary and periodic points for such semigroups.
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