On Random Fixed Point Theory

Dr. Claudio Morales

Department Mathematical Sciences
UAHuntsville

1 October 2010
218 Shelby Center
3:00 (Refreshements at 2:30)

Abstract

All began in the 1950's with a group of mathematicians of the Prague school of probabilists, under the direction of the late Antonin Spacek. They realized that in using operator equations to model various systems, it was not enough just to consider random initial data. It was also necessary to take into consideration that the operator used to describe the behavior of systems might have not been fully known. As a consequence of these observations, the idea of random operators arose. A survey written by Bharucha-Reid in 1976 brought more insights to the theory, generating additional interest on the subject. In our case, we will explore some of the fundamental results of random fixed point theory, such as the stochastic formulation of the Banach contraction principle as well as Schauder fixed point theorem, among others. Various basic definitions will be carefully introduced to reach out to an ample audience.