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The aim of this paper is to prove some existence and uniqueness results of the fixed points for Hardy-Rogers type contraction in cone metric spaces associated with a -distance and endowed with a graph. These results prepare a more general statement, since we apply the condition of orbitally -continuity of mapping instead of the condition of continuity, and consider cone metric spaces endowed with a graph instead of cone metric spaces.doi:10.15393/j3.art.2020.6850 fatcat:ns7ecgybp5dkjaxxkfrzcdfe3q