\documentclass{amsart}
\title{Nonlinear ergodic theorems for nonexpansive semigroups and
solutions of nonlinear evolution equations}
\author{Wataru Takahashi}
\address{Department of Mathematical and Computing Sciences,
Tokyo Institute of Technology,
2-12-1, O-okayama, Meguro, Tokyo 152-8552, Japan}
\email{wataru@is.titech.ac.jp}
\keywords{ergodic theorem, nonexpansive semigroup, evolution equation}
\subjclass[2010]{46T99}
\begin{document}
\maketitle
In this talk, we deal with weak and strong convergence theorems for
families of nonexpansive mappings in Hilbert spaces or Banach spaces. We
first discuss nonlinear weak ergodic theorems for nonexpansive
semigroups in uniformly convex Banach spaces and nonlinear strong
ergodic theorems for nonexpansive semigroups with compact domains in
strictly convex Banach spaces. Next, we deal with weak and strong
convergence theorems for one-parameter nonexpansive semigroups and
accretive operator inclusions in Hilbert spaces or Banach
spaces. Finally, we apply these results to discuss the asymptotic
behavior of solutions of nonlinear evolution equations and the problem
of finding a minimizer of a proper lower-semicontinuous convex function
concerning the proximal point algorithm.
\def\thefootnote{}\footnote{Topics: Nonlinear Functional Analysis}
\end{document}