Robert Brooks, Klaus Schmitt, Brandon Warner
Abstract:
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
Submitted April 20, 2011. Published May 2, 2011.
Math Subject Classifications: 37B055, 37B10, 37L25, 34B15.
Key Words: Fixed sets; function system; self-similar sets;
invariant sets; Hausdorff metric; Hausdorff topology;
boundary value problem
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Robert Brooks Department of Mathematics, University of Utah 155 South 1400 East, Salt Lake City, UT 84112, USA email: brooks@math.utah.edu |
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Klaus Schmitt Department of Mathematics, University of Utah 155 South 1400 East, Salt Lake City, UT 84112, USA email: schmitt@math.utah.edu |
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Brandon Warner Department of Mathematics, University of Utah 155 South 1400 East, Salt Lake City, UT 84112, USA email: brandon.warner@utah.edu |
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