Quasi-asymptotic contractions,set-valued dynamic systems,uniqueness of endpoints and generalized pseudodistances in uniform spaces |
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Authors: | Kazimierz Włodarczyk Robert Plebaniak |
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Institution: | Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of ?ód?, Banacha 22, 90-238 ?ód?, Poland |
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Abstract: | For set-valued dynamic systems in uniform spaces we introduce the concept of quasi-asymptotic contractions with respect to some generalized pseudodistances, describe a method which we use to establish general conditions guaranteeing the existence and uniqueness of endpoints (stationary points) of these contractions and exhibit conditions such that for each starting point each generalized sequence of iterations (in particular, each dynamic process) converges and the limit is an endpoint. The definition, result, ideas and techniques are new for set-valued dynamic systems in uniform, locally convex and metric spaces and even for single-valued maps. |
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Keywords: | 54C60 47H10 54E15 46A03 54E50 |
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