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The purpose of this paper is to present several fixed point theorems for the so-called set-valued Y-contractions. Set-valued Y-contractions in ordered metric spaces, set-valued graphic contractions, set-valued contractions outside a bounded set and set-valued operators on a metric space with cyclic representations are considered.
A number of fixed point theorems are presented for weakly contractive maps which have weakly sequentially closed graph. Our results automatically lead to new existence theorems for differential inclusions in Banach spaces relative to the weak topology.
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