Fixed Point Theory and Applications

, 2010:864536 | Cite as

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

  • Kazimierz Włodarczyk
  • Robert Plebaniak
Open Access
Research Article
Part of the following topical collections:
  1. Impact of Kirk's Results on the Development of Fixed Point Theory


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.


Dynamic System Generalize Sequence Dynamic Process Differential Geometry Convergence Theorem 
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© K.Włodarczyk and R. Plebaniak. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of Nonlinear Analysis, Faculty of Mathematics and Computer ScienceUniversity of ŁódźŁódźPoland

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