“School of Mathematics”
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| Paper IPM / M / 12734 |
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| Abstract: | |
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Here, we show that continuous set-valued maps which are generalized
set contraction on noncompact topological spaces have a maximal invariant (fixed)
set. As an application, we prove the existence and uniqueness of endpoints for
topological contraction mappings. Also, we present fractal set results for system
of continuous set-valued maps on regular topological spaces. As application of
our result, we show how some fixed point theorems can be established from these
results.
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