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By using the notion of the fixed point set of multi-valued mappings, we introduce an equivalence relation on the set of all closed and bounded valued multifunction on a metric space. By using the notion we provide some related results. 2010 Mathematics Subject Classification: 34A08, 34B16.doi:10.17114/j.aua.2018.54.03 fatcat:cgvqam2vtrh77lpez3cigaztau