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Let X ′ be a subposet of a poset X. Define PRE(X,X ′) be the semigroup under composition of all regressive transformations from a subset of X into X ′. Moreover, TRE(X,X ′) = {α ∈ PRE(X,X ′) : domα = X}. In 2012, C. Namnak and E. Laysirikul [3] investigated the Green’s relations on TRE(X) = TRE(X,X). Now, we aim to extend the result of them by study the Green’s relations on the semigroups TRE(X,X ′) and PRE(X,X ′). AMS Subject Classification: 20M20

GREEN'S RELATIONS ON SEMIGROUPS OF REGRESSIVE TRANSFORMATIONS WITH RESTRICTED RANGE