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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 Applications volume 2010, Article number: 864536 (2009) Cite this article

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.

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Authors and Affiliations

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

    Kazimierz Włodarczyk & Robert Plebaniak

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  1. Kazimierz Włodarczyk
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  2. Robert Plebaniak
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Correspondence to Kazimierz Włodarczyk.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Włodarczyk, K., Plebaniak, R. Periodic Point, Endpoint, and Convergence Theorems for Dissipative Set-Valued Dynamic Systems with Generalized Pseudodistances in Cone Uniform and Uniform Spaces. Fixed Point Theory Appl 2010, 864536 (2009). https://doi.org/10.1155/2010/864536

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

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