Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 864536, 32 pages
doi:10.1155/2010/864536

Periodic point, endpoint, and convergence theorems for dissipative set-valued dynamic systems with generalized pseudodistances in cone uniform and uniform spaces

Abstract

In cone uniform and uniform spaces, we introduce the three kinds of dissipative set-valued dynamic systems with generalized pseudodistances and not necessarily lower semicontinuous entropies, we study the convergence of dynamic processes and generalized sequences of iterations of these dissipative dynamic systems, and we establish conditions guaranteeing the existence of periodic points and endpoints of these dissipative dynamic systems and the convergence to these periodic points and endpoints of dynamic processes and generalized sequences of iterations of these dissipative dynamic systems. The paper includes examples.