The fixed point and the common fixed point properties in finite pseudo-ordered sets

Abdelkader Stouti

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Palabras clave


Pseudo-ordered set ; Trellis ; Complete trellis ; Monotone map ; Fixed point property ; Least fixed point property ; Greatest fixed point property ; Common fixed point property

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Referencias


Abian, A., Fixed point theorems of the mappings of partially ordered sets, Rendiconti del Circolo Mathematico di Palermo 20, pp. 139-142, (1971).

Abian, S. and Brown, A. B., A theorem on partially ordered sets with applications to fixed point theorems, Can. J. Math. 13, pp. 78-82, (1961).

Amann, H., Order structures and fixed points, Ruhr-universităt, Bochum, mimeographed lecture notes, (1977).

Baclawski, K., A combinatorial proof of a fixed point property, J. Combin. Theory (A) 119, pp. 994-1013, (2012).

Bourbaki, N., Sur le thorme de Zorn, Arch. Math., 2, pp. 434-437, (1940-1950).

Demarr, R., Common fixed points for isotone mappings, Colloq. Math. 13, pp. 45-48, (1964).

Bhatta, S. P. and Shashirekha, H., A characterisation of completeness for Trellises, Algebra univeralis 44, pp. 305-308, (2000).

Bhatta, S. P., Weak chain completeness and fixed point property for pseudo-ordered sets, Czechoslovac Mathematical Journal, 55 (130), pp. 365-369, (2005).

Bhatta, S. P. and Shiju, G., A note on weak chain-completeness and fixed point property for pseudo ordered sets, Advances in discrete mathematics and applications: Mysore, 2008, 119-123, Ramanujan Math. Soc. Lect. Notes Ser. 13, Ramanujan Math. Soc., Mysore, (2010).

Bhatta, S. P. and Shiju, G., Some fixed point theorems for pseudo ordered sets, Algebra Discrete Math. 11, No. 1, pp. 17-22, (2011).

Brondsted, A., Common fixed points and partial orders, Proc. Amer. Math. Soc. 77, No. 3, pp. 365-368, (1979).

Capard, N., Leclerc, B. and Monjardet B., Finite ordered sets, Concepts, results and uses. Encyclopedia of Mathematics and its Applications, 144. Cambridge University Press, Cambridge, (2012). xii+337 pp.

Knaster, B., Un théorème sur les fonctions d’ensembles, Ann. Soc. Polon. Math. 6 (1928), 133-134.

Lim, T. C., On the largest common fixed point of a commuting family of isotone maps, Discrete and Continuous Dynamical Systems, Series A, Suppl., pp. 621-623, (2005).

Rival, I., A fixed point theorem for finite partially ordered sets. J. Combin. Theory (A) 21(1976), 309-318 (1976).

Schröder, Bernd S. W., Algorithms for the fixed point property, ORDAL ’96 (Ottawa, ON), Theoret. Comput. Sci. 217, No. 2, pp. 301-358, (1999).

Schröder, Bernd S. W., Ordered sets. An introduction, Birkhuser Boston, Inc., Boston, MA, (2003). xviii+391 pp.

Schröder, Bernd S. W., The fixed point property for ordered sets. Arab. J. Math. (Springer) 1, No. 4, pp. 529-547, (2012).

Skala, H. L., Trellis theory, Algebra Universalis 1, pp. 218-233, (1971).

Skala, H. L., Trellis theory, Mem. Amer. Math. Soc. 121, Providence, (1972).

Stouti, A. and Maaden, A., Fixed points and common fixed points theorems in pseudo-ordered sets, Proyecciones 32, No. 4, pp. 409-418, (2013).

Tarski, A., A lattice-theoretical fixpoint theorem and its applications, Proc. Amer. Math. Soc. 5, pp. 285-309, (1955).

Wong, James S. W., Common fixed points of commuting monotone mappings, Canad. J. Math., 19, pp. 617-620, (1967).


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