Fixed set theorems for discrete dynamics and nonlinear boundary-value problems

Fixed set theorems for discrete dynamics and nonlinear boundary-value problems

We consider self-mappings of Hausdorff topological spaces which map compact sets to compact sets and establish the existence of invariant (fixed) sets. The fixed set results are used to provide fixed set analogues of well-known fixed point theorems. An algorithm is employed to compute the existe...

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Bibliographic Details
Main Authors: Robert Brooks, Klaus Schmitt, Brandon Warner
Format: Article
Language:English
Published: Texas State University 2011-05-01
Series:Electronic Journal of Differential Equations
Subjects:
Fixed sets
function system
self-similar sets
invariant sets
Hausdorff metric
Hausdorff topology
boundary value problem
Online Access:http://ejde.math.txstate.edu/Volumes/2011/56/abstr.html
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spelling doaj-82df2c21bdb046b5b0f1e6f5e8b52ae72020-11-24T22:43:26ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-05-01201156,115Fixed set theorems for discrete dynamics and nonlinear boundary-value problemsRobert BrooksKlaus SchmittBrandon WarnerWe consider self-mappings of Hausdorff topological spaces which map compact sets to compact sets and establish the existence of invariant (fixed) sets. The fixed set results are used to provide fixed set analogues of well-known fixed point theorems. An algorithm is employed to compute the existence of fixed sets which are self-similar in a generalized sense. Some numerical examples are given. The utility of the abstract result is further illustrated via the study of a boundary value problem for a system of differential equations http://ejde.math.txstate.edu/Volumes/2011/56/abstr.htmlFixed setsfunction systemself-similar setsinvariant setsHausdorff metricHausdorff topologyboundary value problem
collection DOAJ
language English
format Article
sources DOAJ
author Robert Brooks
Klaus Schmitt
Brandon Warner
spellingShingle Robert Brooks
Klaus Schmitt
Brandon Warner
Fixed set theorems for discrete dynamics and nonlinear boundary-value problems
Electronic Journal of Differential Equations
Fixed sets
function system
self-similar sets
invariant sets
Hausdorff metric
Hausdorff topology
boundary value problem
author_facet Robert Brooks
Klaus Schmitt
Brandon Warner
author_sort Robert Brooks
title Fixed set theorems for discrete dynamics and nonlinear boundary-value problems
title_short Fixed set theorems for discrete dynamics and nonlinear boundary-value problems
title_full Fixed set theorems for discrete dynamics and nonlinear boundary-value problems
title_fullStr Fixed set theorems for discrete dynamics and nonlinear boundary-value problems
title_full_unstemmed Fixed set theorems for discrete dynamics and nonlinear boundary-value problems
title_sort fixed set theorems for discrete dynamics and nonlinear boundary-value problems
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2011-05-01
description We consider self-mappings of Hausdorff topological spaces which map compact sets to compact sets and establish the existence of invariant (fixed) sets. The fixed set results are used to provide fixed set analogues of well-known fixed point theorems. An algorithm is employed to compute the existence of fixed sets which are self-similar in a generalized sense. Some numerical examples are given. The utility of the abstract result is further illustrated via the study of a boundary value problem for a system of differential equations
topic Fixed sets
function system
self-similar sets
invariant sets
Hausdorff metric
Hausdorff topology
boundary value problem
url http://ejde.math.txstate.edu/Volumes/2011/56/abstr.html
work_keys_str_mv AT robertbrooks fixedsettheoremsfordiscretedynamicsandnonlinearboundaryvalueproblems
AT klausschmitt fixedsettheoremsfordiscretedynamicsandnonlinearboundaryvalueproblems
AT brandonwarner fixedsettheoremsfordiscretedynamicsandnonlinearboundaryvalueproblems
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