This term, we focus on fixed point theorems and applications. In many proofs, fixed point arguments are the main arguments. For instance, the Banach fixed point theorem is used to prove the theorem on implicit functions (Analysis 2), the theorem of Picard-Lindelöf (ordinary differential equations), or the Jacobi iteration for the iterative solution of linear systems (Numerical Mathematics).
In this seminar, we are going to discuss the fixed point theorems of Banach, Brouwer, and Schauder. One main concern is on the respective assumptions of these theorems. We will also study counter examples if the assumptions are relaxed. Dependent on the knowledge and interests of the participants, possible applications of fixed point arguments are taken from the analysis and numerics of ordinary or partial differential equations.
If you want to participate and to give a lecture, please contact Dirk Praetorius via email dirk.praetorius@tuwien.ac.at to make an appointment and to fix the topic of a possible talk.
