Báo cáo hóa học: "Research Article Periodic Point, Endpoint, and Convergence Theorems for Dissipative Set-Valued Dynamic Systems with Generalized Pseudodistances in Cone Uniform and Uniform Spaces"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Periodic Point, Endpoint, and Convergence Theorems for Dissipative Set-Valued Dynamic Systems with Generalized Pseudodistances in Cone Uniform and Uniform Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 864536 32 pages doi 2010 864536 Research Article Periodic Point Endpoint and Convergence Theorems for Dissipative Set-Valued Dynamic Systems with Generalized Pseudodistances in Cone Uniform and Uniform Spaces Kazimierz WIodarczyk and Robert Plebaniak Department of Nonlinear Analysis Faculty of Mathematics and Computer Science University of Udi Banacha 22 90-238 Udi Poland Correspondence should be addressed to Kazimierz Wlodarczyk wlkzxa@ Received 29 September 2009 Accepted 17 November 2009 Academic Editor Mohamed A. Khamsi Copyright 2010 K. Wlodarczyk and R. Plebaniak. 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. 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. 1. Introduction A set-valued dynamic system is defined as a pair X T where X is a certain space and T is a set-valued map T X 2X in particular a set-valued dynamic system includes the usual dynamic system where T is a single-valued map. Here 2X denotes the family of all nonempty subsets of a space X. Let X T be a dynamic system. By Fix T Per T and End T we denote the sets of all fixed points periodic points and endpoints of T respectively that is Fix T w e X w e T w .

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