Fixed points theorems for monotone set-valued maps in pseudo-ordered sets

Abstract: In this paper, we first establish the existence of the greatest and the least fixed points for monotone set-valued maps defined on non-empty pseudo-ordered sets. Furthermore, we prove that the set of all fixed points of two classes of monotone set-valued maps defined on a non-empty complete trellis is also a non-empty complete trellis. As a consequence we obtain a generalization of the Skala's result [Theorem 37. Skala, Helen. Trellis theory. Memoirs of the American Mathematical Society, No. 121. American Mathematical Society, Providence, R.I. MR0325474 (48 #3821)].

Keywords: Pseudo-ordered set, fixed point, monotone map, trellis, complete trellis.

Classification (MSC2000): 06B23; 06B05, 54C60, 47H10

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