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
Description
Summary: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
ISSN:1072-6691

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