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In this paper we introduce a new notion, named as D1-space, which is weak than D-metric space and G-metric space. Then several families of generalized contractive type mappings are defined on the D1-space. We then obtain some theorems on the existence of unique common fixed points for these mappings which additionally satisfy the converse commuting condition.doi:10.12732/ijpam.v106i2.18 fatcat:ftk3xoeu3vdwdivhc4jhle437e