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  • Research Article
  • Open Access

Periodic Point, Endpoint, and Convergence Theorems for Dissipative Set-Valued Dynamic Systems with Generalized Pseudodistances in Cone Uniform and Uniform Spaces

Fixed Point Theory and Applications20092010:864536

https://doi.org/10.1155/2010/864536

  • Received: 29 September 2009
  • Accepted: 17 November 2009
  • Published:

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.

Keywords

  • Dynamic System
  • Generalize Sequence
  • Dynamic Process
  • Differential Geometry
  • Convergence Theorem

Publisher note

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Authors’ Affiliations

(1)
Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

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