Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces |
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Authors: | K W?odarczyk C Obczyński D Wardowski |
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Institution: | Department of Nonlinear Analysis, Faculty of Mathematics, University of ?ód?, Banacha 22, 90-238 ?ód?, Poland |
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Abstract: | Set-valued weaker contractions in uniform, locally convex and metric spaces are defined and dynamic systems of such weaker contractions are studied. Conditions guaranteeing the convergence of generalized sequences of random iterations and iterations and the existence and uniqueness of endpoints of set-valued weaker contractions are established. Our definitions and results are new for set-valued maps in uniform, locally convex and metric spaces and even for single-valued maps. |
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Keywords: | Set-valued dynamic system Random iteration Set-valued weaker contraction Motion Endpoint Uniform space |
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