Fixed points and common fixed points theorems in pseudo-ordered sets

 

Abdelkader Stouti, Abdelhakim Maaden
University Sultan Moulay Slimane, Morocco

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ABSTRACT

Under suitable conditions, we establish the existence of the greatest and the least fixed points of monotone maps defined on nonempty pseudo-ordered sets. Also, we prove that the set of all common fixed points of two categories of finite commutative family F of monotone maps f defined on a nonempty complete trellis is also a nonempty complete trellis.

2000 Mathematics Subject Classification : 06B23, 54C60,47H10.

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

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Abdelkader Stouti
Center for Doctoral Studies: Sciences and Techniques,
Laboratory of Mathematics and Applications,
Faculty of Sciences and Techniques,
University Sultan Moulay Slimane,
P. O. Box 523. Beni-Mellal 23000
Morocco
e-mail : stout@fstbm.ac.ma

 

Abdelhakim Maaden
Center for Doctoral Studies: Sciences and Techniques,
Laboratory of Mathematics and Applications,
Faculty of Sciences and Techniques,
University Sultan Moulay Slimane,
P. O. Box 523. Beni-Mellal 23000
Morocco

Received : May 2011. Accepted : July 2013.