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

  • Abdelkader Stouti University Sultan Moulay Slimane.
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

Resumen

Biografía del autor/a

Abdelkader Stouti, University Sultan Moulay Slimane.
Center for Doctoral Studies: Sciences and Techniques, Laboratory of Mathematics and Applications, Faculty of Sciences and Techniques.

Citas

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

[2] 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).

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

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

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

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

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

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

[9] 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).

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

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

[12] 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.

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

[14] 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).

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

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

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

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

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

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

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

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

[23] Wong, James S. W., Common fixed points of commuting monotone mappings, Canad. J. Math., 19, pp. 617-620, (1967).
Publicado
2018-03-15
Cómo citar
Stouti, A. (2018). The fixed point and the common fixed point properties in finite pseudo-ordered sets. Proyecciones. Journal of Mathematics, 37(1), 1-18. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2777
Sección
Artículos